Math ATI/ Pocket Prep

There is an 8.75 % sales tax on a shirt that costs $30. Which of the following is the correct estimate of the final sale price after tax is added? (round to the nearest dollar.)

$33 To solve: 0.0875 x 30 = 2.625 2.625 + 30 = 32.325

Solve: 5/6 × 2/3 = x

(5×2)/(6×3) = 10/18. = 5/9

Solve the following by subtracting. 2 1/3 - 3/4 =

1 7/12

Given that 4 centimeters = 1.5748 inches, how many centimeters are in one foot?

1 foot × 12 inches/1 foot × 4 centimeters/1.5748 inches = 30.48 centimeters (cm).

Rachel has 1 gallon of gasoline. How many ounces of gasoline does she have?

1 gallon × 4 quarts (qt.)/1 gallon (gal) × 2 pints (pt.)/1 qt. × 2 cups (c)/ 1 pt. × 8 ounces (oz.)/1 c Therefore 1 gallon = 1 × 4 × 2 × 2 × 8 = 128 oz.

If Don weighs 250 pounds, what is his approximate weight in kilograms?

1 kilogram (kg) is approximately 2 pounds (lb.): 250 lb. × 1 kg / 2 lb. = 125 kg

$1 US is equivalent to about 6.56 Chinese yuan. A two -bedroom Presidential suite on the top floor of a high-end hotel in Shanghai, China was listed at 25,000 yuan per night. What is the cost of this suite per night in US dollars?

3,810.98 To solve: 25,000 x 1 / 6.56 = 3,810.98

Convert 3.5 pounds to ounces.

3.5 pounds × 16 ounces / 1 pound = 3.5 × 16 = 56 ounces.

The operations manager is designing a new office layout and assumes 3 office chairs per 2 desks. How many office chairs will be needed for an office building with 30 desks?

3⋅30 = 2⋅x 2x = 90 x = 90/2 = 45 chairs

A number is six more than quadruple a given number. How would this phrase be translated into a mathematical expression?

4 × n = 4n Six more' means to add 6 to this number. =4n + 6

Convert 4.3 liters into milliliters.

4.3 liters(L) × 1,000 milliliters(mL)/1 L = 4,300 mL.

Using the table to find the answer, what is the conversion of 16 fl. oz. to ml.?

473.18 mL To solve : 16 x 29.57353 = 473.17648

If Jacob can draw 4 caricatures in 52 minutes, how long will it take him to draw 84 caricatures?

4x = 52 ⋅ 84 x = 1,092 minutes Convert minutes to hours. 60x = 1,092 x = 18.2 hours find the number of minutes. 60 × 0.2 = 12 = 18 hours 12 minutes

Sarah wants to put a 1.5 foot wide painting in the middle of a 12 foot wide wall. She wants the painting to be exactly horizontally centered on the wall. What should the distance be, in feet, from either side of the wall to the edge of the painting?

5.25 feet To solve: x + 1.5 + x = 12 2x = 12-1.5 10.5 / 2 = 5.25

Convert 5.75 pounds to ounces.

5.75 pounds(lb.) × 16 ounces(oz.)/1 lb. = 92 oz.

Alice is installing carpet in 5 rooms. If each room requires 550 square feet of carpet, how much total carpet is needed?

550 square feet (ft2)/ 1 room × 5 rooms = 550×5 = 2750 ft2.

Simplify the following: 2 2/5 + 4 1/3

6 11/15

Of the 2,716 cars sold in the last quarter, Charles sold 679. What percentage of the cars sold did Charles sell?

679 ÷ 2716 = 0.25 Convert this to a percentage 0.25 × 100 = 25%

Which of the following percent's is equivalent to 0.78

78% 0.78 = 78/100

A box has a volume of 792 in3. If two sides are 8 in and 9 in, what is the length of the third side?

792 = 8⋅9⋅c so the third side c = 792/72 = 11 inches.

Two trees are in Abby's backyard. One tree is 20 feet tall and casts a shadow 8 feet long. If the second tree's shadow at the same time of day 32 feet?

80 Ft To solve: 32x20 =640 8/640 = 80

The data below shows the performance of five students on a test: 72%, 64%, 81%, 78%, 75% The student who scored 75% on the test approached the teacher for re-grading. The teacher awarded a 6% increase in her score. What was her new score?

An increase of 6% is equivalent to multiplying 75 × 1.06 = 79.5% =80%.

Amber has 3 red flowers. Betty has 7 red flowers and 2 yellow flowers. If Betty gives Amber one third of her flowers including both yellow flowers, how many red flowers does Amber end up with?

Betty has 7+2 = 9 flowers in total, meaning that 1/3 of that amount will be 3 flowers. Since 2 will be yellow, the remaining 1 must be red. Thus Amber ends up with 3+1 = 4 red flowers.

Express 432 cubic inches as a percentage of 1 cubic foot.

Convert 1 cubic foot (ft3) to cubic inches (in3). 1 foot = 12 inches, so 1 foot3 = 123 inches3 = 1728 cubic inches. Divide to find the percentage. To find the percentage, divide 432/1728, multiply by 100, and add a percentage sign. 432/1728 = 0.25, so this 432 is 25% of 1 cubic foot.

If a wound requires a stitch every 1cm, approximately how many stitches does a 4-inch wound require?

Convert 4 inches to cm. Since 1 inch is approximately 2.5 cm, use a unit conversion fraction: 4 in × 2.5 cm/1 in = 10 cm. Convert cm into stitches. Since each cm requires 1 stitch, 10cm corresponds to 10 stitches.

The furniture in the dollhouse was designed on a 1:30 scale of the original furniture. If an original bed measured 5 feet by 8 feet, what are the measurements of the bed in the dollhouse?

Convert the feet measurements to inches. To convert from feet to inches, multiply by 12. Thus 5 feet = 60 inches and 8 feet = 96 inches, so the 5' × 8' bed measures 60" × 96". Divide by the scale factor. Since the scale is 1:30, multiply each dimension by 1/30. This gives 60/30 × 96/30 = 2" x 3.2".

Which of the following represents 3/25 as a decimal?

Correct answer: 0.12

3/4 is how many times greater than 1/2?

Divide (3/4)/(1/2). = 6/4. reduces to 3/2. = 1 1/2 times greater.

Solve the following by dividing and reducing to the lowest common denominator. 7/9 ÷ 2/5 =

Divide the fractions. 35/18 Write as a mixed number. 35/18 = 1 17/18

A rectangular dining room table is 3.5 feet wide by 8 feet long. What is the perimeter of the table?

The perimeter is 2 × Length + 2 × Width. In this case, that is 2×8 + 2×3.5 = 23 feet.

Jonathan mowed around the perimeter of the football field. The field was 360 feet long by 150 feet wide. If Jonathan mowed two laps around the field, how many feet did he mow?

The perimeter of a rectangle 2⋅Length + 2⋅Width 2⋅360 + 2⋅150 = 1,020 feet. Two laps will be this multiplied by 2 2⋅1020 = 2,040 feet.

If Mike walks around the edge of a pool that is 20 feet wide and 110 feet long four times, how far has he walked in total?

The perimeter of a rectangle is 2×Length + 2×Width 2×20 + 2×110 = 260 feet for each trip around. Since Mike makes 4 trips around the pool, 4×260 = 1,040 feet in total.

What is the perimeter of a rectangle with a length of 11 and a width of 17?

The perimeter of a rectangle is 2×Length + 2×Width. 2×11 + 2×17 = 22 + 34 = 56.

A triangle's three sides are labeled AB, BC, and AC. AB's length is 5x + 2. BC's length is x + 3. AC's length is 3x - 1. What is the perimeter of the triangle?

The perimeter of the triangle is AB + BC + AC, (5x+2) + (x+3) + (3x-1). Combine the x terms (5x+x+3x) + (2+3-1), = 9x + 4.

90% To solve: 85 +5 = 90%

The pie chart shows the percentages of residents in a town based on political party affiliation . What percent of residents are not Democrats?

If the diameter of a circle is 50 inches, what is the radius in inches?

The radius is half the diameter. In this case, half of 50 inches =25 inches.

Two angles in an isosceles triangle are 80° and 50°. What is the measure of the third angle?

The sum of angles in a triangle must be 180° 80°+50°+x° = 130 x = 50°

Alisha purchased a new vehicle for $32,500 and she was responsible for paying the $2,112.50 sales tax at the title office. What is the percentage sales tax that Alisha paid on her new vehicle?

The tax proportion is $2,112.50 / $32,500 = 0.065 0.065 × 100% = 6.50%

A box is 5 inches long, 8 inches wide, and has a volume of 320 cubic inches. What is the height of the box?

The volume of a box is given by the formula Length × Width × Height. This means that 320 in3 = 5 in × 8 in × Height, meaning Height = 320 in 3/40 in2 = 8 in.

0.68 million views/ month To solve: 3.4 million viewer / 5 months = 0.68 (4.2 - 8) million viewers / (6-1) months

This line graph show rating of a television show from January- June 2008. What is the average rate of change in number of viewers over time from January to June?

Place the following list of numbers in order, from least to greatest. 1/5, 1/8, 9/16, 5/16, 3/5

convert the fractions to decimals. 1/5 = 0.21/8 = 0.1259/16 = 0.56255/16 = 0.31253/5 = 0.6 Order the decimals from least to greatest. 0.125, 0.2, 0.3125, 0.5625, 0.6 or 1/8, 1/5, 5/16, 9/16, 3/5.

A car salesman sold 33 cars on Saturday. If the salesman sold twice as many convertibles as he did sedans that day, how many sedans did he sell on Saturday?

the total number of cars is S+C = 33. If twice as many convertibles were sold, then C = 2S. Solve for S. S+2S = 333 S = 33 Divide both sides by 3S = 33/3 = 11 sedans

A company produces rectangular cookie boxes. Which of the following is the estimated volume of a box with a length of 8.5 cm, a height of 10.1 cm, and a width and 3.3 cm, if each dimension is rounded to the nearest centimeter.

270 cm3 To solve: 9cm x 3cm x 10 cm = 270 cm3

When the sum of 1.8912 and 3.1846 is rounded to the nearest hundredth, the result is:

1.8912 + 3.1846 = 5.0758 Since the 5 digit in the thousandths place indicates that you need to round up, = 5.08.

Elizabeth works 12 hours per week and earns $10.50 per hour. 20% of her paycheck is taken for taxes and other withholdings. How much money does Elizabeth take home in a two-week period?

12 × $10.50 = $126 for each week. Since there are two weeks, 2 × $126 = $252. Find the taxes for the period. She pays 20% taxes on $252, which is a total of 0.20 × $252 = $50.40 Subtract. $252 - $50.40 = $201.60.

The sum of two unequal numbers is 20,560. The smaller number is 3,745. What is the larger number?

16,815 To solve: 20,560-3,745

What is the least denominator of the following fractions 2/9, 1/2, 2/3

18

If sounds travels 6,160 feet in 5.5 seconds, how far does it travel in 16.5 seconds?

18,480 Ft To solve: 16.5 x 6,160 / 5.5 =18,480

One hand is defined to be 4 inches. The largest horse ever measured-Goliath-was approximately 20.5 hands tall. How tall was Goliath in inches?

20.5 hands × 4 in/1 hand = 82 in.

Which of the following fractions is used to express 22% in the lowest terms?

22% = 22/100. = 11/50

A school bake sale sells 4% of its cookies to the first customer. There are 24 cookies left. How many cookies did the bake sale have to start?

25 X stands for the number of cookies To solve: (1-0.04) = 0.96 x = 24/0.96 X =25

A rancher increased her herd of cattle to 360 head form 288 head. What was the percent increase in cattle?

25% To solve: 360-288 =72 72/288 = x 0.25 = x

Jack mixed salt and sugar in a ratio of 2:3 in a container to investigate its taste and other characteristics. If the total weight of the mixture was 115 grams, how many more grams of sugar were added than grams of salt?

Find the amount of salt. Since there are a total of 2+3 = 5 parts, each part is 115/5 = 23 grams. Since there are 2 parts salt, there are 2×23 = 46 grams of salt. Find the amount of sugar. Since each part is 23 grams and there are 3 parts sugar, there are 3×23 = 69 grams of sugar. Subtract. There are 69 - 46 = 23 more grams of sugar than grams of salt.

A company bought baseball tickets for 84 employees and 33 guests. If the employee tickets each cost $40 and each guest ticket cost $30, how much did the company pay in total?

Find the cost of the employee tickets. Each employee ticket costs $40, so 84 of them cost 84×$40 = $3,360. Find the cost of the guest tickets. Each guest ticket costs $30, so 33 of them cost 33×$30 = $990. Find the total. The total cost is the sum of these two costs, or $3,360 + $990 = $4,350.

A rock weighing 654 pounds contains 120 pounds of zinc and 360 pounds of iron. What is the percentage of the iron in the rock?

Find the fraction of iron in the rock. The fraction of iron is 360/654. Convert the fraction to a percentage. 360/654 = 0.55. To convert to a percentage, multiply by 100 and add a % sign, = 55%

Color A is generated by mixing various color pigments. The constituent color pigments p, q and r are mixed in the ratio of 2:3:4 respectively to make 0.027 pints of color A. What is the required amount of pigment q?

Find the fraction of the whole that A represents. The total number of parts is 2+3+4 = 9, so q corresponds to 3/9 parts or 1/3 of the total. Find the amount corresponding to that fraction. 1/3 of the total is 1/3 * 0.027 = 0.009 pints.

A class has 24 students. If the number of boys is 10, what is the ratio of girls to boys?

Find the number of girls. The number of girls is 24-10 = 14. Write a ratio. Girls: Boys is 14:10 Reduce the ratio to the lowest terms. divide both by 2 to get 14:10 = 7:5.

The class of 32 children had 14 boys and the remainder were girls. What was the ratio of boys to girls?

Find the number of girls. The number of girls will be Total - Boys, giving 32-14 = 18 girls. Write the Boys: Girls ratio. The ratio is 14:18. Reduce to lowest terms. 14 and 18 share a factor of 2. Dividing both by 2 gives = 7:9.

Virginia has been teaching third grade seven hours a day, five days a week, for the last twenty weeks. How many minutes has she been teaching?

Find the number of hours Virginia has been teaching. 7 hours/day × 5 days/week × 20 weeks = 700 hours. Convert to minutes. 700 hours × 60 minutes/1 hour = 42,000 minutes.

A rectangle is 1 foot by 2 feet. What is the perimeter of the rectangle?

Find the perimeter. 2×Length + 2×Width = 2×1 + 2×2 = 6 feet. Convert to inches. 6 feet × 12 inches/1 foot = 72 inches

What is the perimeter of a rectangle with length 11 inches and width 4 inches?

Find the perimeter. 2×Length + 2×Width, 2×11 + 2×4 = 30 inches. Convert to feet and inches. Divide by 12 30 = 12×2 + 6, so 30 inches = 2 feet 6 inches.

45% of gross domestic product of a country is contributed by agriculture. Write an expression showing the total amount of contribution made by all other sectors of production.

Identity the percentage made by all other sectors. 100% - 45% = 55% Convert the percentage to an expression. 55/100 ⋅ x. Write the expression in lowest terms. = 11x/20.

A graph shows that each year Susan's income goes up by a certain percentage. Which factor is dependent?

Income

The perimeter of a soccer field is 328 m. The length is 36m greater that the width. What are the length and width of the soccer fields?

Length: 100 m Width: 64 m To solve: 2(W +36) + 2W = 328 4W +72 = 328-72 = 256 4W / 265 = 64 W = 64 L = 64 + 36 = 100

Find the result of the following operation: Multiply 3/4 by itself then subtract the result from 1.

Multiply 3/4 by itself.(3/4)×(3/4) = 9/16. Subtract from 1. 1 - 9/16. 16/16 - 9/16 = (16-9)/16 = 7/16.

Simplify 54% of $350.

Multiply and simplify. 54% × $350 = 0.54 × 350 = $189

A graph shows that the population of a country goes up each year from 1990 through 2020. Which of the following is (are) the dependent variable(s)?

Population

Solve: 2:x = 22:121

Rewrite the ratios as fractions 2/x = 22/121 Cross-multiply to eliminate the denominators. 242 = 22x Solve for x. x = 242/22 = 11.

The distance between points A and B on a map is 7 inches. If two inches on a map represents 56 yards, how far is point A from point B in yards?

Set up a proportion. 2 inches/56 yards = 7 inches/x yards Cross-multiply to eliminate denominators. 2⋅x = 56⋅7 = 392 Solve for x .2x = 392x = 392/2 = 196 yards

Simplify 25% of (3/4 - 1/2)

Simplify 3/4 - 1/2. = 1/4. Write both 25% as a fraction. 25% is the same as 1/4 Multiply the fractions. 25/100 × 1/4 = 1/16

Convert 1.88 meters to centimeters.

Since 1 meter = 100 centimeters 1.88 meters × 1 meter/100 centimeters = 188 centimeters.

Adam weighs 210 pounds. Approximately how many kilograms (kg) does Adam weigh?

Since 2 pounds (lb.) equal to 1 kilogram (kg) 210 lb. × 1 kg/2 lb. = 105 kg.

The product of two numbers is 4.536. If one of the numbers is 0.9, what is the other number?

Since the product is 4.536 and one of the numbers is 0.9 0.9 ⋅ x = 4.536 x = 4.536 ÷ 0.9 = 5.04

|3 + x| = 5 Which of the following options is the correct solution set for the above equation?

Solve the first equation for x. 3 + x = 5x = 5 - 3x = 2 Solve the second equation for x. 3 + x = -5x = -5 - 3x = -8 Write the solution set. Since x can be 2 or -8, the solution set is {-8, 2}.

A weather balloon rises through the atmosphere and records the temperature for every 100m increase in elevation. What is the dependent variable(s) in this scenario?

Temperature

If the radius of a circle is 12.5 inches, what is the diameter of the circle?

The diameter of a circle is twice the length of the radius. 12.5 inches × 2 = 25 inches

If x is 35% more than 60, what is x?

To increase by 35%, multiply by 1 + 35/100 = 1.35. Thus x = 1.35⋅60 = 81.

Convert 2.25 pounds to ounces

Use a unit conversion fraction. 2.25 pounds(lb.) × 16 ounces(oz.)/1 lb. = 36 oz.

How many minutes are there in five weeks?

Use unit conversion fractions 5 weeks × 7 days/1 week × 24 hours/1 day × 60 minutes/1 hour = 50,400 minutes.

7.6 cm To solve: 6 tick marks past 7cm = 7.6 cm long

What is the length of the rectangle?

252.6075

Which of the following is a product of multiplying twenty-seven and twenty-five hundredths by nine and twenty-seven hundredths.

The longer the eruption, the longer the waiting time between eruptions.

Which of the following observations about volcanic eruptions is correct based on the scatterplot?

15 To solve: 9 x 9 = 81 and 12 x 12 = 144 81 + 144 = 225 225 squared = 15

Which of the following the length of side C?

How would 1.05 be displayed as a fraction?

Write 1.05 as an improper fraction. 1.05 = 100/100 + 5/100 = 105/100. Simplify the fraction. 105 and 100 share a factor of 5, so divide both by 5 =21/20

The product of two numbers is 11.88. One number is 0.6. What is the other number?

Write an equation based on the information given. If x is the unknown second number, then 11.88 = 0.6⋅x. Solve for x. Divide both sides by 0.6, giving x = 11.88/0.6 = 19.8.

65% of citizens of a town were satisfied with the performance of their mayor. If 2,145 citizens were satisfied with the mayor, how many total citizens are in the town?

Write an equation describing the percentage. The unknown number of citizens in the town is 0.65⋅x = 2145. Solve for x. = 2145/0.65 = 3,300 citizens.

In the first three games of the season, the Rockets scored 74, 71, and 82 points. If their average score after 4 games is 77 points, how many points did they score in the fourth game?

Write an equation for the average. Solve for x. 74+71+82=227 Multiply both sides by 4 77⋅4 = 308. Now subtract 227 from both sides 308 - 227 = 81 points.

Find x by solving the following proportion. 12:22::x:121

Write the proportions as a fraction equation. 12/22 = x/121 Solve for x. 12⋅121 = 1452 = 1452/22 = 66

34 To solve: 20 + 14 = 34

based on information from the table, which of the following is the number of students who wrote more than 3 thank you notes?