Hesi Math Study Guide 2021-2022

Find the ratio of $2.8 and $1.4

$2.8 : $1.4 = (2.8 ⋅ 10) : (1.4 ⋅ 10) $2.8 : $1.4 = 28 : 14 $2.8 : $1.4 = 2 : 1 Hence, the ratio of $2.8 and $1.4 is 2 : 1.

Write the given verbal phrase into mathematical expression "One fifth of sum of 3 times a number and 9"

(3x + 9) / 5

Write the given verbal phrase into mathematical expression "One seventh of 3 less than 4 times a number

(4x - 3) / 7

-36 °C =

-32.8

-23 °C

-9.4 C

1 / 5

.20 = 20 %

1 / 4

.25 = 25 %

3 * 10

.30 = 30 %

7 mg

0.00007 hg

33 mL

0.00033 hL

2 cL

0.002 dkL

43 mg

0.0043 dkg

7 mg

0.007 g

2 mm

0.02 dm

4 / 0.14

0.035

8 / 0.56

0.07

0.4 / 0.0304

0.076

0.10 / 0.008

0.08

8 g

0.08 hg

30 cg

0.3 g

8 / 2.816

0.352

5 mm

0.5 cm

6.1x 0.1

0.61

2 / 1.28

0.64

2 / 1.43

0.715

5 / 4.055

0.811

C to F

1 Celsius = (?) Fahrenheit

1 milliliter = ?

1 cc

2.54 centimeters = ?

1 inch

If A's salary is 20% less than B's salary. By what percent is B's salary more than A's salary ?

B's salary is 25% more than A's salary.

If x : 2 and 5 : 6 are inverse to each other, find the value of "x"

Because the given two ratios are inverse to each other, the product of the two ratios is equal 1. (x : 2) ⋅ (5 : 6) = 1 (x/2) ⋅ (5/6) = 1 5x / 12 = 1 x = 12 / 5

If the absolute value equation |x - 3| - k = 0 has the solution x = -5, find the value of k.

Because x = -2 is a solution, substitute x = -2 in the given absolute value equation. |-5 - 3| - k = 0 |-8| - k = 0 8 - k = 0 8 = k

If the absolute value equation |2x + k| = 3 has the solution x = -2, find the value of k.

Because x = -2 is a solution, substitute x = -2 in the given absolute value equation. |2(-2) + k| = 3 |-4 + k| = 3 Solve for k : -4 + k = 3 or -4 + k = -3 k = 7 or k = 1

0.003C = 1.317

C = 1.317 ÷ 0.003C = 439

0.4C = 15.2

C = 15.2 ÷ 0.4C = 38

Two numbers are in the ratio 7 : 9 and their least common multiple is 378. Find the numbers.

Two numbers are in the ratio 7 : 9 and their least common multiple is 378. Find the numbers.

The area of a rectangle is x2 + 4x -12. What are the dimensions of the rectangle (length and width)?

Since the length is usually longer, length = x + 6 and width = x + -2

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ? (excluding the one at start)

15 times

5.7+ 9.3

15.5

MDXXXIV

1534

MDLXV

1565

MDLXXXVIII

1588

6.8+ 9.2

16

1 gallon

16 cups

1 pound = ? ounces

16 oz

1.5 / 25.05

16.7

1 mile

1760 yards

2 / 36.0

18

65 °F =

18.3 °C

0.06 / 108

1800

MDCCCXXX

1830

0100

1:00 AM

1300

1:00 PM

1 pint = ?

2 cups

Find the ratio of 2 hours and 115 minutes.

2 hours = 2 ⋅ 60 = 120 minutes 2 hrs : 115 min = 120 min : 115 min 2 hrs : 115 min = 24 : 23 Hence, the ratio of 2 hours and 115 minutes is 24 : 23.

1 quart = ?

2 pts

Use distributive property to solve the problem below:Maria bought 10 notebooks and 5 pens costing 2 dollars each.How much did Maria pay?

2 × (10 + 5) = 2 × 10 + 2 × 5 = 20 + 10 = 30 dollars

Write the given verbal phrase into mathematical expression "2 times the sum of 7 times a number and 4"

2(7x + 4)

1 ton = ?

2,000 lbs

1 pound = ? kilograms

2.2 kg

1 kilogram

2.2 pounds

0.4 / 0.916

2.29

.2 =

2/10 = 1/5

3.0x 6.9

20.70

9 / 191.7

21.3

9 / 207.0

23

MMCDXXX

2430

25cm

250 mm

MMDXCVI

2596

26 cL

260 mL

0200

2:00 AM

1400

2:00 PM

1 yard = ?

3 ft

Write the given verbal phrase into mathematical expression "7 less than 3 times the sum of a number and 6"

3(x + 6) - 7

Write the given verbal phrase into mathematical expression "One fourth of 3 times the difference between a number and 6"

3(x - 6) / 4

Write the given verbal phrase into mathematical expression "3 times the difference between a number and 8"

3(x - 8)

11.78- 8.66

3.12

2.3x 1.4

3.22

0.24 / 0.7872

3.28

0.02 / 0.069

3.45

37 cg

3.7 dg

1 oz = ? mm

30 mm/cc

9.8x 3.13

30.38

6.6x 4.8

31.68

MMMCLV

3155

MMMCLXXXV

3185

32 kg

32000 g

1 / 3

33 1/3%

.34 =

340/1000 = 17/50

34 hL

3400000 mL

100 °F =

37.8 °C

38 hg

3800 g

0.27 / 10368

38400

.397 =

397/1000

0300

3:00 AM

1500

3:00 PM

At the store beef jerky is $44.25 for 3 pounds. If you buy 4 pounds, how much will it cost ?

4 pounds of beef jerky will cost $59

1 gallon = ? quarts

4 qts

4 / 17.56

4.39

0.5 / 2.365

4.73

0.9 / 4.365

4.85

6.5x 6.3

40.95

40 dkL

400000 mL

6.9x 6.3

43.47

0.23 / 10.534

45.8

7.1x 6.6

46.86

.465 =

465/1000 = 93/200

47 dm

470 cm

0400

4:00 AM

1600

4:00 PM

Write the given verbal phrase into mathematical expression "7 less than 4 times a number"

4x - 7

1 mile = ? feet

5,280 ft

0500

5.00 AM

0.2- 4.9

5.3

7.0- 1.7

5.3

3.4+ 2.1

5.5

13.27- 7.66

5.61

3 / 17.37

5.79

3 / 17.91

5.97

1 / 2

50%

A person can cover a distance of 84 miles in 4 gallons of fuel. If he has 2.5 gallons, how many miles can he cover ?

52.5 miles traveled in 2.5 gallons of fuel.

12 °C =

53.6 °F

.54 =

54/100 = 27/50

5 / 9

55 5/9%

0.18 / 10.152

56.4

4 / 7

57 1/7%

0.020 / 11500

575000

.59 =

59/100

1700

5:00 PM

Write the given verbal phrase into mathematical expression "The sum of 5 times a number and 8"

5x + 8

Write the given verbal phrase into mathematical expression "5 times of a number is decreased by 8"

5x - 8

18 is taken away from 8 times of a number is 30. Find the number.

6

43 °F =

6.1 °C

12.4- 5.6

6.8

3.3 / 22.902

6.94

0.8x 8.7

6.96

.6 =

6/10 = 3/5

6 dL

60 cL

1.0 / 6070

6070

1.8 * 113.4

63

.637 =

637/1000

18 °C

64.4 °F

64 =

640/1000 = 16/25

.66 =

66/100 = 33/50

0600

6:00 AM

1800

6:00 PM

Write the given verbal phrase into mathematical expression "6 times of a number is increased by 15"

6x + 15

3.7+ 3.3

7

9.3- 2.1

7.2

0.19 / 1.4383

7.57

14.34- 6.71

7.63

15.65- 7.66

7.99

1.9 / 13623

7170

8 / 11

72 8/11%

0.32 / 24288

75900

7 / 9

77 7/9 %

11 / 14

78 4/7%

26 °C

78.8 °F

26C to F

78.8F

0700

7:00 AM

1900

7:00 PM

1 cup = ?

8 oz

0.8 / 6.784

8.48

17.4- 8.8

8.6

16.05- 7.38

8.67

0.010 / 8030

803000

7 / 601.3

85.9

0.3 / 258

860

0800

8:00 AM

2000

8:00 PM

If 5 men can paint a house in 18 hours, how many men will be able to paint it in 10 hours ?

9 men will be able to paint the house in 10 hours.

9 dkm

90 m

0.024 / 2160

90000

0900

9:00 AM

2100

9:00 PM

MCDXIII

1413

1 kilogram = ?

1,000 grams

1 kilometer = ?

1,000 m

1 gram = ?

1,000 mg

1 liter = ?

1,000 mm

1 mile = ? yards

1,760 yards

4 / 4.96

1.24

6 / 9.00

1.5

0.3x 5.0

1.50

1 hg

10 dkg

1 centimeter = ?

10 mm

7.38+ 2.94

10.32

1 meter = ?

100 cm

1000

10:00 AM

2200

10:00 PM

1.3+ 9.7

11.0

8.32+ 2.83

11.15

6.84+ 4.48

11.32

6.09+ 5.30

11.39

Solve for n : 11.7 = 1.1 + n

11.7 = 1.1 + n Subtract 1.1 from each side. 10.6 = n So, the value of n is 10.6.

1100

11:00 AM

2300

11:00 PM

1 foot = ?

12 in

54 °F =

12.2 °C

5.3+ 7.5

12.8

MCCXXIII

1223

1 gallon = ? ounces

128 oz

0000

12:00 AM

1200

12:00 PM

7 men can complete a work in 52 days. In how many days will 13 men finish the same work?

13 men can complete the work in 28 days.

0.20 / 2700

13500

If thrice of A's age 6 years ago be subtracted from twice his present age, the result would be equal to his present age. Find A's present age.

A's present age is 9 years.

A fast food restaurant had 7 boxes of chicken nuggets for $25.90. A competing restaurant had 3 boxes of chicken fingers for $11.07. Which food has a higher unit price ?

Comparing the unit prices, chicken nugget has a higher unit price.

At the market you can buy 5 bags of apples for $23.60. At the orchard you can get 7 bags of apples for $32.76. Which is the better deal ?

Comparing the unit prices, orchard has lower price. So buying apples in orchard is better deal.

A store had 4 blue chairs for $73.48 or 5 red chairs for $91.40. Which color chair has a lower unit price ?

Comparing the unit prices, red color chair has a lower unit price

Find the compound ratio of 2 : 3, 9 : 4 and 5 : 6.

Compound ratio of 2 : 3, 9 : 4 and 5 : 6 is = (2 ⋅ 9 ⋅ 5) : (3 ⋅ 4 ⋅ 6) = 90 : 72 = 5 : 4 Hence, the compound ratio of 2 : 3, 9 : 4 and 5 : 6 is 5 : 4.

0.02 D + 3.89 = 6.75

D = 143

0.02 D + 3.54 = 10.16

D = 331

If David can prepare 2 gallons of juice in 4 days, how many cups of juice can he prepare per day ?

David can prepare 8 cups of juice in 1 day.

Find the duplicate ratio of 5 : 6.

Duplicate ratio of 5 : 6 is = 5² : 6² = 25 : 36 Hence, the duplicate ratio of 5 : 6 is 25 : 36.

Evaluate the given expression for x = 3 and y = 5. 3x + 2y

Evaluate the given expression for x = 3 and y = 5. 3x + 2y Answer :

0.5 F + 0.74 = 238.24

F = 475

Find the least common multiple of the following two fractions. 8/21, 6/35

Formula to find the least common multiple of fractions : = LCM of Numerators / HCF of Denominators *LCM -----> least common multiple *HCF -----> highest common factor LCM of numerators (8, 6) = 24 HCF of denominators (21, 35) = 7 Least common multiple of (8/21, 6/35) is = 24/7

At the toy store you could get 2 board games for $8.36. Online the price for 3 board games is $12.84. Which place has the highest price for a board game ?

From the above comparison, it is clear that online has the highest price for a board game.

Two numbers are in the ratio 2 : 3. If 4 be subtracted from each, they are in the ratio 3 : 5. Find the numbers.

From the given ratio 2 : 3, we have first number = 2x second number = 3x From the information "If 4 be subtracted from each, they are in the ratio 3:5", we have (2x-4) : (3x-4) = 3:5 Using cross product rule of proportion, we have 5(2x-4) = 3(3x-4) 10x - 20 = 9x - 12 x = 8 Therefore, the first number = 2(8) = 16 the second number = 3(8) = 24

The length and width of a rectangle is in the ratio 3 : 5. If its perimeter is 48 cm, find its length and width.

From the given ratio, we have length = 3x and width = 5x Perimeter = 48 2(l + w) = 48 2(3x + 5x) = 48 8x = 24 x = 3 Therefore, Length = 3(3) = 9 cm Width = 5(3) = 15 cm

0.3 H + 3.81 = 133.11

H = 431

A merchant has 120 liters and 180 liters of two kinds of oil. He wants to sell the oil by filling the two kinds in tins of equal volumes. Find the greatest volume of such a tin.

Hence, the greatest volume of the tin is 60 liters

In a triangle, the second angle is 5° more than the first angle. And the third angle is three times of the first angle. Find the three angles of the triangle.

Hence, the three angles of the triangle are 35°, 40° and 105°.

Solve for x : 5 + x = 3

Here 5 is added to the variable x. To get rid of 5, we have to subtract 5 from each side of the equation as shown below. So, the value of x is -2.

Solve for m : (1/4)m = 3

Here m is divided by 4. To get rid of 4, we have to multiply each side of the equation by 4 as shown below. So, the vale of m is 12.

Solve for m : 38 - m = -44

Here m is having negative sign. In this problem, first we have to make m to be positive. For that, we have to add m to each side of the equation. When we do so, we will have "-44 + m" on the right side of the equation. Then, to get rid of -44 on the right side, we have to add 44 to each side of the equation. Therefore, we have to add m and 44 to each side of the given equation. Then, 82 = m So, the value of m is 82.

Solve for p : 8 - p = 12

Here p is having negative sign. In this problem, first we have to make p to be positive. For that, we have to add p to each side of the equation. When we do so, we will have "12 + p" on the right side of the equation. Then, to get rid of 12 on the right side, we have to subtract 12 from each side of the equation. Therefore, we have to add p and subtract 12 on both sides and solve the equation as shown below. So, the vale of p is -4.

Solve for r : 2r = 6

Here r is multiplied by 2. To get rid of 2, we have to divide each side of the equation by 2 as shown below. So, the vale of r is 3.

Find the highest common factor of the numbers 0.045 and 0.075

In the given two numbers 0.045 and 0.075, we find equal number of digits after the decimal point. That is, three digits. To get rid of the decimal point, we have to multiply each number by 1000. 0.045 ⋅ 1000 = 45 0.075 ⋅ 1000 = 75 Find the greatest common factor 45 and 75 using prime factorization method. Write the prime factors of 45 and 75 as shown below. 45 = 3 ⋅ 3 ⋅ 5 75 = 3 ⋅ 5 ⋅ 5 The prime factors that are common to 45 and 75 are 3 and 5 Product of common prime factors : = 3 ⋅ 5 = 15 HCF (45, 75) = 15. Divide the HCF 15 by 1000. 15 / 1000 = 0.015 So, the greatest common factor of 0.045 and 0.075 is 0.015

0.008J = 1.584

J = 1.584 ÷ 0.008J = 198

0.07J = 2.59

J = 2.59 ÷ 0.07J = 37

If John can cover 360 miles in 3 hours, find the number of miles covered by John in 1 minute.

John can cover 2 miles in 1 minute.

0.005K = 2.49

K = 2.49 ÷ 0.005K = 498

0.008L = 2.432

L = 2.432 ÷ 0.008L = 304

0.4 L + 2.07 = 168.07

L = 415

0.009 L + 2.4 = 2.895

L = 55

Find the least common multiple of 6, 7 and 15 by division method.

LCM (6, 7, 14) = Product of all prime factors = 2 ⋅ 7 ⋅ 3 = 42

The LCM of two numbers is 432 and their HCF is 36. If one of the numbers is 108, then find the other number.

Let x be the other number. We know that, the product of the two numbers is = LCM ⋅ HCF Then, 108 ⋅ x = 432 ⋅ 36 Divide each side by 108. x = (432 ⋅ 36) / 108 x = 144 The other number is 144.

David earns $416 in 8 hours. How much does earn in 2.8 hours?

Mr. David will earn $145.6 in 2.8 hours.

0.8 N + 2.77 = 399.57

N = 496

0.6P = 23.4

P = 23.4 ÷ 0.6P = 39

0.08 P + 2.98 = 8.1

P = 64

A football team lost 5 yards and then gained 9. What is the team's progress?

Progress = -5 + 9 = 4 yards

If $1000 is divided among the three people in the ratio 2:3:5, find the share of each.

Share of the first person = 2x Share of the second person = 3x Share of the third person = 5x Total Amount = $1000 That is, 2x + 3x + 5x = 1000 10x = 1000 x = 100 Therefore, Share of the first person = 2(100) = $200 Share of the second person = 3(100) = $300 Share of the third person = 5(100) = $500

Alex takes 15 days to reduce 30 kilograms of his weight by doing 30 minutes exercise per day. If he does exercise for 1 hour 30 minutes per day, how many days will he take to reduce the same weight ?

So, if Alex does exercise for 1 hour 30 minutes per day, it will take 5 days to reduce 30 kilograms of weight.

A video game store was getting rid of old games, selling them 3 for $56.28. If they sold 7 games, how much money would they have made ?

So, if they sold 7 games, they would they have made $131.32

Solve the absolute value equation : 0.5|0.5x| - 0.5 = 2.5

Solve : 0.5|0.5x| - 0.5 = 2.5 Add 0.5 to each side. 0.5|0.5x| = 3 Divide each side by 0.5 |0.5x| = 6 0.5x = 6 or 0.5x = -6 x = 12 or x = -12

2|3x +4| = 7

Solve : 2|3x +4| = 7 Divide each side by 2. |3x + 4| = 7/2 3x + 4 = 7/2 or 3x + 4 = -7/2 3x = 7/2 - 4 or 3x = -7/2 - 4 3x = -1/2 or 3x = -15/2 x = -1/6 or x = -15/6 x = -1/6 or x = -5/2

3|5x - 6| - 4 = 5

Solve : 3|5x - 6| - 4 = 5 Add 4 to each side. 3|5x - 6| = 9 Divide each side by 3. |5x - 6| = 3 5x - 6 = 3 or 5x - 6 = -3 5x = 9 or 5x = 3 x = 9/5 or x = 3/5

Solve the absolute value equation : |2x + 5| + 6 = 7

Solve : |2x + 5| + 6 = 7 Subtract 6 from each side. |2x + 5| = 1 2x + 5 = 1 or 2x + 5 = 1 2x = -4 or 2x = -6 x = -2 or x = -3

Solve the absolute value equation : |3x + 5| = 7

Solve : |3x + 5| = 7 3x + 5 = 7 or 3x + 5 = -7 3x = 2 or 3x = -12 x = 2/3 or x = -4

Solve the absolute value equation : |7x| = 21

Solve : |7x| = 21 7x = 21 or 7x = -21 x = 3 or x = -3

Solve the absolute value equation : |x - 3| + 6 = 6

Solve : |x - 3| + 6 = 6 Subtract 6 from each side. |x - 3| + 6 = 6 Subtract 6 from each side. |x - 3| = 0 x - 3 = 0 or x - 3 = 0 x = 3 or x = 3

Solve the absolute value equation : |x² - 4x - 5| = 7

Solve : |x2 - 4x - 5| = 7 x2 - 4x - 5 = 7 or x2 - 4x - 5 = -7 x2 - 4x - 12 = 0 or x2 - 4x + 2 = 0 Solve the first quadratic equation x² - 4x - 12 = 0. x2 - 4x - 12 = 0 (x + 2)(x - 6) = 0 x + 2 = 0 or x - 6 = 0 x = -2 or x = 6 Solve the second quadratic equation x² - 4x + 2 = 0. This quadratic equation can not be solved using factoring. Because the left side part can not be factored. So, we can use quadratic formula and solve the equation as shown below. So, the solution is x = -2, 7, 2 ± √2.

Solve for v : -25.7 - v = -40.3

Solve for v : -25.7 - v = -40.3

Evaluate the given expression for m = 1/3. 18m2 + 3m + 7

Substitute 1/3 for m into the given expression. 18m2 + 3m + 7 = 18(1/3)2 + 3(1/3) + 7 18m2 + 3m + 7 = 2 + 1 + 7 18m2 + 3m + 7 = 10

Evaluate the given expression for m = 13. m2 + m - 54

Substitute 13 for s into the given expression. m2 + m - 54 = 132 + 13 -54 m2 + m - 54 = 169 + 13 - 54 m2 + m - 54 = 128

Evaluate the given expression for x = 2 and y = -5. x2 - 3y2

Substitute 2 for x and -5 for y into the given expression. x2 - 3y2 = 2(2)2 - 3(-5)2 x2 - 3y2 = 2(4) - 3(25) x2 - 3y2 = 8 - 75 x2 - 3y2 = -77

Evaluate the given expression for m = 3. (2m2 + 5m - 7) / 2

Substitute 3 for m into the given expression. (2m2 + 5m - 7) / 2 = [2(3)2 + 5(3) - 7] / 2 (2m2 + 5m - 7) / 2 = [2(9) + 15 - 7 ] / 2 (2m2 + 5m - 7) / 2 = (18 + 15 - 7) / 2 (2m2 + 5m - 7) / 2 = 26 / 2 (2m2 + 5m - 7) / 2 = 13

Evaluate the given expression for x = 3 and y = 5. x2 + y2

Substitute 3 for x and 5 for y into the given expression. x2 + y2 = 32 + 52 x2 + y2 = 9 + 25 x2 + y2 = 34

Evaluate the given expression for m = 5 and n = 2. 5m2 + 2m2n

Substitute 5 for m and 2 for n into the given expression. 5m2 + 2m2n = 5(5)2 + 2(5)2(2) 5m2 + 2m2n = 5(25) + 2(25)(2) 5m2 + 2m2n = 125 + 100 5m2 + 2m2n = 225

Evaluate the given expression for m = 5 and n = 2. m2 + 2mn2

Substitute 5 for m and 2 for n into the given expression. m2 + 2mn2 = 52 + 2(5)(2)2 m2 + 2mn2 = 25 + 40 m2 + 2mn2 = 65

Evaluate the given expression for s = 5. s2 + 7s - 2

Substitute 5 for s into the given expression. s2 + 7s - 2 = 52 + 7(5) - 2 s2 + 7s - 2 = 25 + 35 - 2 s2 + 7s - 2 = 58

Evaluate the given expression for s = 6. s2 - 3s + 10

Substitute 6 for s into the given expression. s2 - 3s + 10 = 62 - 3(6) + 10 s2 - 3s + 10 = 36 - 18 + 10 s2 - 3s + 10 = 28

F to C

Subtract 32 from the Fahrenheit temperature. Multiply this number by five. Divide the result by nine.

0.007T = 1.008

T = 1.008 ÷ 0.007T = 144

0.3 T + 2.8 = 37.9

T = 117

0.7 T + 3.77 = 195.57

T = 274

Find the inverse ratio of 12 : 13.

The inverse ratio of 12 : 13 is 13 : 12

A wine seller had three types of wine. 403 liters of 1st kind, 434 liters of 2nd kind and 465 liters of 3rd kind. Find the least possible number of casks of equal size in which different types of wine can be filled without mixing.

The least possible number of casks of equal size required is 42.

Therefore, length = 6 and width = x - 2 = 6 - 2 = 4

The numbers are 10 and 6

Find the highest common factor (HCF) of the numbers 48 and 64 using division method.

The product of common factors of 48 and 64 is = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 8

Find the least common multiple (LCM) of 7 and 12.

There is no common divisor for 7 and 12. So, 7 and 12 are relatively prime. The least common multiple of two numbers that are relatively prime is product of those two numbers. Hence, the least common multiple of 7 and 12 is = 7 ⋅ 12 = 84

Since the length is usually longer, length = x + 6 and width = x + -2

Therefore, length = 6 and width = x - 2 = 6 - 2 = 4

Theresa wants new carpeting for her family room. Her family room is a 12 ft by 21 ft rectangle. How much carpeting does she need to buy to cover her entire family room ?

Theresa needs to buy 252 square ft carpeting to cover her entire family room.

Find the triplicate ratio of 2 : 3.

Triplicate ratio of 2 : 3 is = 2³ : 3³ = 8 : 27 Hence, the triplicate ratio of 2 : 3 is 8 : 27.

Find the highest common factor of the numbers 18, 24 and 30 by factor tree method.

Using factor Tree Method, find the factors of 18, 24 and 30. The factors of 18 are 1, 2, 3, 6, 9 and 18. The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30. The factors that are common to all numbers 18, 24 and 30 are 1, 2, 3, 6 In the above common factors, 6 is the largest value. So, HCF (18, 24, 30) = 6.

0.4V = 158.8

V = 158.8 ÷ 0.4V = 397

0.6W = 205.8

W = 205.8 ÷ 0.6W = 343

What is the greatest number that will divide 62, 78 and 109 leaving remainders 2, 3 and 4 respectively ?

When 62, 78 and 109 are divided by the greatest number, leaving remainders 2, 3 and 4 respectively. Then, 62 - 2 = 60 78 - 3 = 75 109 - 4 = 105 Get all the common factors of 60, 75 and 105 and see that the common factors will divide them all. The greatest number is the HCF of 60, 75 and 105. The product of common factors of 60, 75 and 105 is = 3 ⋅ 5 = 15 So, HCF (60, 75, 105) = 15. Hence, the HCF is 15, which is the greatest number that will divide 62, 78, 109 leaving remainders 2, 3 and 4 respectively.

Find the least common multiple of 18 and 24 using prime factorization method.

Write the prime factors of 18 and 24. 18 = 2 ⋅ 3 ⋅ 3 24 = 2 ⋅ 2 ⋅ 2 ⋅ 3 The prime factor 2 appears a maximum of 3 times in the prime factorization of 24. The prime factor 3 appears a maximum of 2 times in the prime factorization of 18. LCM (18, 24) = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 = 72

Find the highest common factor of the numbers 84 and 182 by prime factorization method.

Write the prime factors of 42 and 91 as shown below. 84 = 2 ⋅ 7 ⋅ 2 ⋅ 3 182 = 2 ⋅ 7 ⋅ 13 The prime factors that are common to 84 and 182 are 2 and 7 Product of common prime factors : = 2 ⋅ 7 So, HCF (84, 182) = 14.

0.001 X + 1.79 = 2.025

X = 235

The width of the rectangle is 2/3 of its length. If the perimeter of the rectangle is 80 cm. Find its area.

area of the rectangle is 384 square cm.

Find the least number of soldiers in a regiment such that they stand in rows of 15, 20, 25 and form a perfect square.

the least number of soldiers required is 900.

Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely.

the least number of square tiles required is 344,864.

A piece of iron rod costs $60. If the rod was 2 meter shorter and each meter costs $1 more, the cost would remain unchanged. What is the length of the rod?

the length of the given rod is 12 m.

The length of a rectangle is 4 less than 3 times its width. If its perimeter is 32 cm, then find the area of the rectangle.

he area of the rectangle is 55 square cm.

If a person drinks 8 cups of apple juice per month, how many gallons will he drink in one year?

he will drink 6 gallons of apple juice in 1 year.

A book contains 120 pages and each page has 35 lines. How many pages will the book contain if every page has 24 lines per page ?

if every page has 24 lines per page, the book will contain 175 pages.

A truck covers a particular distance in 3 hours with the speed of 60 miles per hour. If the speed is increased by 30 miles per hour, find the time taken by the truck to cover the same distance

if the speed is increased by 30 mph, time taken by the truck is 2 hours.

At the baseball stadium the price for popcorn is $5.88 for 3 bags. If you want to buy 7 bags of popcorn, how much will it cost ?

if we want to buy 7 bags of popcorn, it will cost $13.72

A train is running at a speed of 20 m/sec.. If it crosses a pole in 30 seconds, find the length of the train in meters.

length of the train is 600 meters.

Solve for m : m - 10 = -15

m - 10 = -15 Add 10 to each side. m = -5 So, the value of m is -5.

The sum of two consecutive even integers is 26. What are the two numbers?

n = 6

The poster has a border whose width is 2 cm on each side. If the printed material has the length of 6 cm and width of 8 cm, then find the area of the border.

the area of the border is 72 square cm.

75 basketballs cost $1143.75. Find the cost of 26 basketballs.

the cost of 26 basket balls is $ 396.50

A manufacturer produces 80 units of a product at a cost of $22000 and 125 units at a cost of $28750. Assuming the cost curve to be linear, find the equation of the cost curve and then use it to estimate the cost of 95 units.

the cost of 95 units is $24250.

In a business, if A can earn $7500 in 2.5 years, At the same rate, find his earning for 4 years.

the earning for 4 years is $12000.

For a certain commodity, the demand equation giving demand "d" in kg, for a price "p" in dollars per kg. is d = 100(10 - p). The supply equation giving the supply "s" in kg. for a price "p" in dollars per kg is s = 75(p - 3). Find the equilibrium price.

the equilibrium price is $7.

If the numerator of a fraction is increased by 2 and the denominator by 1, it becomes 1. In case, the numerator is decreased by 4 and the denominator by 2, it becomes 1/2. Find the fraction.

the fraction is 7/8.

Two trains running at 60 kmph and 48 kmph cross each other in 15 seconds when they run in opposite direction. When they run in the same direction, a person in the faster train observes that he crossed the slower train in 36 seconds. Find the length of the two trains (in meters).

the length of the two trains are 330 m and 120 m.

It takes 20 seconds for a train running at 54 kmph to cross a platform.And it takes 12 seconds for the same train in the same speed to cross a man walking at the rate of 6 kmph in the same direction in which the train is running. What is the length of the train and length of platform (in meters).

the lengths of the train and platform are 160 m and 140 m respectively.

In 36.5 weeks, Miguel raised $2,372.50 for cancer research. How much money will he raise 20 weeks ?

the money raised in 20 weeks is $1300.

When the price of a product was decreased by 10 % , the number sold increased by 30 %. What was the effect on the total revenue ?

the net effect in the total revenue is 17% increase.

A park charges $10 for adults and $5 for kids. How many many adults tickets and kids tickets were sold, if a total of 548 tickets were sold for a total of $3750 ?

the number of adults tickets sold is 202 and kids tickets is 346.

The hypotenuse of a right angled triangle is 20 cm. The difference between its other two sides is 4 cm. Find the length of the sides.

the other two sides of the triangle are 12 cm and 16 cm.

A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation ?

the percentage error in the calculation is 64%.

Y is older than X by 7 years. 15 years back X's age was 3/4 of Y's age. Find the present their present ages.

the present ages of "x" and "y" are 36 years and 43 years.

John paid $64 for an item after 20% discount. Find the price of the item without discount.

the price of the item without discount is $80.

The denominator of a fraction exceeds the numerator by 5. If 3 be added to both, the fraction becomes 3/4. Find the fraction.

the required fraction is 12 / 17.

Difference between a number and its positive square root is 12. Find the number.

the required number is 16.

A number consists of two digits. The digit in the tens place is twice the digit in the units place. If 18 be subtracted from the number, the digits are reversed. Find the number.

the required number is 42.

The fourth part of a number exceeds the sixth part by 4. Find the number.

the required number is 48.

The sides of an equilateral triangle are shortened by 12 units, 13 units and 14 units respectively and a right angle triangle is formed. Find the length of each side of the equilateral triangle

the side of the equilateral triangle is 17 units.

The traffic lights at three different road crossings change after every 48 sec, 72 sec and 108 sec respectively. If they all change simultaneously at 8:20:00 hours, when will they again change simultaneously ?

the signals will change simultaneously at 8:27:12 seconds.

If the speed of a train is 20 m/sec, find the speed the train in kmph.

the speed of the train is 72 kmph.

A number consists of three digits of which the middle one is zero and the sum of the other digits is 9. The number formed by interchanging the first and third digits is more than the original number by 297.Find the number.

the three digit number is 306.

Lily to wants to do fencing around a circular garden that has a radius of 70 m. If the cost of fencing is $12 per meter, find the total cost of fencing for the entire garden (Use π = 22/7).

the total cost of fencing for the entire garden is $5280.

In an election, a candidate who gets 84% of votes is elected by majority with 588 votes. What is the total number of votes polled ?

the total number of votes polled 700.

Divide 25 in two parts so that sum of their reciprocals is 1/6.

the two parts of the 25 are 10 and 15.

75 basketballs cost $1,143.75. Find the unit rate in price per basketball

the unit rate in price per basket ball is $ 15.25

In 36.5 weeks, Miguel raised $2,372.50 for cancer research. How was his unit rate in price per week ?

the unit rate in price per week was $65.

In a business, if A can earn $7500 in 2.5 years, find the unit rate of his earning per month

the unit rate of his earning per month is $250.

The length of a train is 300 meter and length of the platform is 500 meter. If the speed of the train is 20 m/sec, find the time taken by the train to cross the platform.

time taken by the train to cross the platform is 40 seconds.

Solve for v : v + 5/3 = - 1/3

v + 5/3 = - 1/3 Subtract 5/3 from each side. v = -2 So, the value of v is -2.

The book fair had a sale where 6 books were $20.46. If you wanted to buy 7 books, how much money would you need ?

we need $23.87 to buy 7 books.

Half a number plus 5 is 11.What is the number?

x = 12

Peter has six times as many dimes as quarters in her piggy bank. She has 21 coins in her piggy bank totaling $2.55

x = 36 x = 6 × 3 = 18Therefore Peter has 3 quarters and 18 dimes

A customer pays 50 dollars for a coffee maker after a discount of 20 dollarsWhat is the original price of the coffee maker?

x = 70

The ratio of two numbers is 5 to 1. The sum is 18. What are the two numbers?

y = 3 x = 5y = 5 × 3 = 15