GRE math word problems

94 ((82+74+90+x)/4)= 85)

Ellen has received the following scores on 3 exams: 82, 74, and 90. What score will Ellen need to receive on the next exam so that the avg score for the 4 exams will be 85?

3

(√3)^2 =

c

10. The product of two consecutive positive integers is 156. What is the greater of the two integers? A) 11 B) 12 C) 13 D) 14 E) 15

3 (6a^2 = 294 -> 7 = x+4 -> x =3)

11) The surface area of a cube with side length (x + 4) is 294. What is the value of x?

c

12) Phillip has twice as many tropical fish as Jody. If Phillip gave Jody 10 of his tropical fish, he would have half as many as Jody. How many tropical fish do Phillip and Jody have together? a) 10 b) 20 c) 30 d) 40 e) 60

d

13) What is the value of 'a' if a+1 a +2 ---- - ------ = 0? a- 3 a -4 a) -2 b) -1 c) 0 d) 1 e) 2

5 (part = % x whole)

15 is 300% of what number?

1,456

An investment in a mutual fund increased by 12% in a single day. If the value of the investment before the increase was $1,300, what was the value after the increase?

a) 1 b) undefined

Rule 4: a) 7^0 b) 0^0

a) 216 (6^3) b) 1,000z^3 ((10z)^3 = 10^3z^3)

Rule 5: a) (2^3)(3^3) b) (10z)^3

a) 9/16 b) r^3/64t^3

Rule 6: a) (3/4)^2 b) (r/4t)^3

y = -4/3x + 13/3 y = -1/2x + 1

Solve the following equations for y in terms of x 4x + 3y = 13 x + 2y = 2

105 (part = % x whole)

find 30% of 350

3 hours (1st part: d = 30t 2nd part (time on interstate): 225 - d = 70(3.5-t) final (putting both expressions together): 225 = 30t + 70(3.5 - t) -> t = 1/2 (1st part of trip) 3.5-1/2 = 3-> Bill spent 3 hours on interstate (2nd part of trip)

https://edu.gcfglobal.org/en/algebra-topics/distance-word-problems/1/ Bill took a trip to see a friend. His friend lives 225 miles away. He drove in town at an average of 30 mph, then he drove on the interstate at an average of 70 mph. The trip took three-and-a-half hours total. How far did Bill drive on the interstate?

27 miles (1. (part 1- going to work): d = 36t 2. (part 2- leaving work): d =27(1.75-t) 3. 36t = 27(1.75-t) -> t = .75 4. plug 't' in for one of the equations; d = 36(0.75)-> d = 27)

https://edu.gcfglobal.org/en/algebra-topics/distance-word-problems/1/ Eva drove to work at an average speed of 36 mph. On the way home, she hit traffic and only drove an average of 27 mph. Her total time in the car was 1 hour and 45 minutes, or 1.75 hours. How far does Eva live from work?

2 hours (1. faster person, Dani: d = 70t; slower person, Jon: 270-d = 60t 2. plug in '70t' for d in Jon equation and get t = 2)

https://edu.gcfglobal.org/en/algebra-topics/distance-word-problems/1/ Jon and Dani live 270 miles apart. One day, they decided to drive toward each other and hang out wherever they met. Jon drove an average of 65 mph, and Dani drove an average of 70 mph. How long did they drive before they met up?

4 hours (1. fast train: d =60t; slow train: 420-d = 45t 2. plug in 60t in for 'd' in slow train equation and get t = 4)

https://edu.gcfglobal.org/en/algebra-topics/distance-word-problems/1/ Pawnee and Springfield are 420 miles apart. A train leaves Pawnee heading toward Springfield at the same time a train leaves Springfield heading toward Pawnee. One train is moving at a speed of 45 mph, and the other is moving 60 mph. How long will they travel before they meet?

80(%) (How I solved: have y = 10 and go from there: .1(50)= 5-> 50(.8)= 4 so 80% is the answer)

https://www.manhattanprep.com/gre/blog/gre-problem-log-quant/ If y≠0, what percent of y percent of 50 is 40 percent of y?

-plane flew for 2 hours at 105 and 3 hours at 115 (Using "d = rt", the first row gives me d = 105t and the second row gives me: 555 - d = 115(5 - t) Since the two distances add up to 555, I'll add the two distance expressions, and set their sum equal to the given total: 555 = 105t + 115(5 - t) Then I'll solve: 555 = 105t + 575 - 115t; 555 = 575 - 10t-20 = -10t -> 2 = t According to my grid, "t" stands for the time spent on the first part of the trip, so my answer is "The plane flew for two hours at 105 mph and three hours at 115 mph.")

https://www.purplemath.com/modules/distance.htm A 555-mile, 5-hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?

1/100 (2/20 x 2/20 OR 1/10 x 1/10)

A person rolls a 20-sided die two times. What are the odds that both of the rolls result in 19s or 20s?

11 (First we divide n'/3=2, cross multiplying them gives, n'=6. when we divide n''/5=1 cross multiplying gives n''=5. finally we add n'+n''= 6+5=11.)

Ex. 15: When the positive integer 'n' is divided by 3, the remainder is 2, and when 'n' is divided by 5, the remainder is 1. What is the least possible value of 'n'?

3.1m^2 (A = 1/2r^2θ -> 1.2(2.1)^2(1.4))

Find the area of the sector formed by a central angle of 1.4 radians in a circle of radius 2.1 meters.

$120 (1. j = 0.3y -> (1-.7= 0.3) b = 0.6x -> (1-.4 = 0.6) b = 12 + j b + j = 84 2. 36 = 0.3y -> y = 120)

Marcy bought one pair of jeans at 70% off, and one blouse at 40% off. If she paid $12 more for the blouse than for the jeans, and she spent a total of $84, what was the original price of the jeans?

√6

Multiply. Write your answer in simplest form. √3 x √2

3√5

Multiply. Write your answer in simplest form. √3 x √15

7√10

Multiply. Write your answer in simplest form. √35 x √14

153/190 (18/20 x 17/19) (Underneath that surface-level veneer, though, arises a sneaky little trick. As we pull bulbs out of the box, we change the odds of what's left in it. If you've got a good bulb in one hand, that's one fewer good bulb that might be in the other hand. To solve this problem, you have 18 good bulbs to choose from (18/20), but even if you're pulling them out simultaneously, there are only 17 other good bulbs that might be in your other hand. So the odds change to 17 out of 19.)

Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective? Give your answer as a fraction

e (That's not an excited 25 in there, it's 25 factorial. 25! Means: 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 And it's this part of the problem that sets up a classic GRE trap. If you were to approach this problem by calculating 25!, you'd either have a calculator with an error screen (too many digits)... If they'd given us 25 as an answer choice, I bet you'd know immediately that it divided evenly into 25!. Same thing if they gave us 24 or 23 or any of the other smaller numbers listed above. They're right there in the product, so they could be divided out evenly. The same thing is true about the answer choices they gave us, if you break them down into smaller products like so: A) 26 = 13 x 2 B) 28 = 14 x 2 C) 36 = 12 x 3 D) 56 = 7 x 8 E) 58 = 29 x 2 4 of the choices are made out of factors on our list. They'll all divide evenly into 25!. Only one of them contains factors that aren't on our list for 25! Answer choice E contains a 29, which is a prime number bigger than 25. It won't be found anywhere between 1 and 25 and it can't be broken down any further than it is. That makes E the correct choice here.)

What is the least positive integer that is not a factor of 25! and is not a prime number a) 26 b) 28 c) 36 d) 56 e) 58

8.6% (part/whole = 12.9/150 = 0.086 = 8.6% *OR* part = percent x total (think: PPW))

What percent of 150 is 12.9?

3 (√18/2 = √9 = 3)

√18/√2

√4√6 = 2√6

√24 =

√30

√3 √10

√ab

√a √b =

6/5 hours or 1 hour and 12 mins (1/3 + 1/2 = 1/x -> 5/6 = 1/x and 6/5 = x; cross multiply to get 6/5)

A batch of computer parts consists of 'n' identical parts, where 'n' is a multiple of 60. Working alone at its constant rate, machine A takes 3 hrs to produce a batch of computer parts. Working alone at its constant rate, machine B takes 2 hrs to produce a batch of computer parts. How long will it take the 2 machines, working simultaneously, to produce a batch of computer parts?

7.2 g of oil (see p. 55; (0.4)(12)/(12+x) = 0.25 ->x = 7.2)

A mixture of 12g of vinegar and oil is 40% vinegar, where all of the measurements are by weight. How many grams of oil must be added to the mixture to produce a new mixture that is only 25% vinegar?

$36 per share

Ex. 12: A stock is valued at $40 per share. If the value increases by 20% and then decreases by 25%, what will the value of the stock per share be after the decrease?

a) (2^2)(3)(31) b) 1, 2, 3, 4, 6, 12, 31, 62, 93, 124, 186, 372

Ex. 4: a) What is the prime factorization of 372? b) What are the *positive* divisors of 372?

a) 2, 5 b) 2, 3

Ex. 5: a) What are the *prime* divisors of 100? b) What are the prime divisors of 144?

(3^2)(5)(13)

Ex.7: What is the prime factorization of 585?

a) 1/64 b) 1/x^10

Exponent rule 1: a) 4^-3 = b) x^-10 =

a) 729 (3^2+4 = 3^6) b) y^2

Exponent rule 2: a) (3^2)(3^4) = b) (y^3)(y^-1) =

a) 125 (5^7-4) b) 1/t^5 (t^-5-> 1/t^5)

Exponent rule 3: a) 5^7/5^4 b) t^3/t^8

1) x^a+b 2) x^a-b 3) 1/x^a 4) 1

Exponential Laws: 1) x^a × x^b = 2) x^a/x^b = 3) x^-a = 4) x^0 =

$10,300 (1. V = P(1 + rt) 2. V = 10,000(1 + .06(1/2))

If $10,000 is invested at a simple annual interest rate of 6%, what's the value of the investment after half a year?

1.14s

If John's present salary 's' is increased by 14%, then write how his new salary can be represented algebraically

P = $902 (answer to nearest dollar) (1. V = P(1+r)^t -> bc compounded *annually* 2. $1,000 = P(1+0.035)^3)

If an amount 'P' is invested at an annual interest rate of 3.5%, compounded annually, what should be the value of 'P' so that the value of the investment is $1,000 at *the end* of 3 years?

25% (amount increase/base = 750-600/600 = 150/600 = 25%)

If an employee's salary increases from 600 to 750, then what is the percent increase

about 37.8 mins (p. 56; d = rt or t =d/r) (51)(40/60) = (54)(x/60))-> set equations equal to each other bc both drive the same distance

In a driving competition, Jeff and Dennis drove the same course at avg speeds of 51 miles per hour and 54 miles per hour, respectively. If it took Jeff 40 mins to drive the course, how long did it take Dennis?

5√2

Multiply. Write your answer in simplest form. √5 x √10

2.48% decrease (1) 100-8% = 92%-> 0.92 2) 100+6% = 106% -> 1.06 3) (1.06)(0.92n) = 0.9752n 4) 100%-97.52% = 2.48%)

On Sept 1, 2013, the # of children enrolled in a certain preschool was 8% less than the # enrolled on Sept 1, 2012. On Sept 1, 2014, the # enrolled was 6% greater than the # enrolled on Sept 1, 2013. By what % did the # of students enrolled change from Sept 1, 2012 to Sept 1, 2014?

a) 1,024 b) 9y^12

Rule 7: a) (2^5)^2 b) (3y^6)^2

7x/2

Simplify (7x^2 + 14x)/2x + 4

√5/3√2

Simplify the number (1/√2)/(3/√5)

x+3/4

Simplify x^2-9/4x-12

x = 1/2ln(3/5)

Solve 5e^2x = 3 for x

c = 3

Solve for c if 2^(3c+1) = 2^10

x < 11.5 (therefore the solution set of the inequality consists of all numbers less than 11.5) (1. Multiply both sides by 11 2. Subtract 9 from both sides 3. Divide both sides by 4)

Solve the inequality (4x+9)/11 < 5

-the solutions are 2/5 and -1 (factored as (5x-2)(x+1))

Solve the quadratic equation 5x^2 + 3x - 2 = 0 by factoring

-the solutions are -3/2, and 2 (1. (2x+3)(x-2) 2. Set each = to 0)

Solving quadratic equations by factoring: Some quadratic equations can be solved more quickly by factoring. Solve 2x^2 - x - 6 = 0 by factoring.

-the selling price must be greater than $46.40 (1. 500(y-30) > 8,200 -bc there's 500 radios being produced, *each* radio will cost $30 to be produced and *each* radio will be sold at another price 'y' -'y-30' instead of '30-y' bc 'y,' the cost, must be greater than the selling price to produce a profit - equation is set > 8,200 bc you want the price 'y' to be at a price where profits exceed $8,200) (*google additional algebraic expression word problems to add to quizlet)

To produce a particular radio model, it costs a manufacturer $30 per radio, and it is assumed that if 500 radios are produced, all of them will be solved. What must be the selling price per radio to ensure that the profit (revenue from the sales minus the total production cost) on the 500 radios is greater than $8,200?

y = -1, x = 4

Use substitution (or elimination) to solve the following system of two equations: 4x + 3y = 13 x + 2y = 2

x = -3/2, 2 (two different solutions bc of the +/-) (a = 2, b = -1, c = -6)

Use the quadratic formula to solve for the quadratic equation 2x^2 - x - 6 = 0

x = -2 (only one solution bc square root of 0 and 0 is neither neg. or pos.)

Use the quadratic formula to solve for the quadratic equation x^2 + 4x + 4 = 0

8.6% (part/whole = 12.9/150 = 0.086 = 8.6%)

What % of 150 is 12.9?

all real numbers except for 6 (bc 12/0 isn't defined)

What's the domain of the following function: f(x) = 2x/x-6

-all real numbers x such that x > (or = to) -2 (square root can't = 0)

What's the domain of the following function: g(x) = x^3 + (√x+2) - 10

all real numbers

What's the domain of the following function: h(x) = |x|

x^2 + y^2 = 100

Write the equation of a circle that has a radius of 10

y-1/4

Write the following algebraically: If 'y' gallons of syrup are to be distributed among 5 people so that one particular person gets 1 gallon and the rest of the syrup is divided equally among the remaining 4, then the # of gallons of syrup that each of the 4 people will get can be represented by algebraically...

1) 4 (bc 3^4 = 81) 2) -2

Write the following logarithmic equations in exponential form: 1) log(base 3)(81) = 2) log (base 7)(1/49) =

d (First, calculate the ending value of Leon's investment. At the end of the first year, that is $100(1 + 0.20) = $100(1.20) = $120. At the end of the second year, it is $120(1.05) = $126. At the end of the third year, it is $126(1 − 0.3) = $126(0.70) = $88.20, and at the conclusion of year four, $88.20(1.20) = $105.84. Cecilia withdraws 10% of her holdings at the end of each year; that means that she leaves only 90% in. The value of her fund at the end of Year 4 is: $200(1.2)(0.9)(1.05)(0.9)(0.7)(0.9) (1.2)(0.9) = $138.88. Now compute Cecilia's amount as a percentage of Leon's: 138.88 105.84 × = 100% 131% (to the nearest percent). (D) is correct) *note: can set up both equations like Cecilia's w/o any addition*

Year 1: +20% Year 2: +5% Year 3: -30% Year 4: +20% 9) Leon invested some of his savings in a mutual fund at the beginning of Year 1, and Cecilia invested twice as much in the same investment at the same time. The annual increases or decreases in the value of the fund are shown in the table above. Cecilia withdrew 10% of the value of her fund at the end of each year, but Leon let his earnings or losses accumulate. To the nearest percent, the value of Cecilia's investment at the end of Year 4 was what percent of the value of Leon's investment? a) 31% b) 66% c) 76% d) 131% e) 139%

a) 6√5 (90 isn't a perfect square; 6 comes from 36 and 5 comes from 5 x 36 equating 180) b) 5√3

a) Simplify √180 b) Simplify √75

a) 6xz√2xz

a) Simplify √72x^3z^3

a) 4b√5 b) 4b^3√3b (b^7 = (b^3)^2 x b) c) 10y^2√2

a) Simplify √80b^2 b) Simplify √48b^7 c) Simplify √200y^4

1/a

a^-1 = ...

5π/6 (note: 6 is the common denominator; π/2+π/3 = 3π/6+2π/6=5π/6)

add the numbers π/2 and π/3

undefined

if x < 0, then √x =

interval

in 2 < x < 3, the set of all real numbers that are between 2 and 3 is called an ...

no

is 1 considered a prime #?

1, 2, 4, 5, 10, 20, 25, 50, 100

list the positive factors of 100

6x^7 + 10x^5 - 3x^2 - 5

multiply (3x^2 + 5)(2x^5 - 1)

13

p. 57: At a fruit stand, apples can be purchased for $0.15 each and pears for $0.20 each. At these rates, a bag of apples and pears was purchased for $3.80. If the bag contained 21 pieces of fruit, how many of the pieces were pears?

-the least interest rate is 4.9% per year compounded quarterly (1. V = P(1+(r/100(n))^nt -> bc compounded 'n' times per year) 2. 20,000(1 + (r/400)^4 ≥ 21,000 3. divide both sides by 20,000 to get -> (1 + r/400)^4 ≥1.05 4. take the fourth root of both sides to get -> 1 + (r/400) ≥ 1.01 5. subtract 1 from both sides to get -> r/400 ≥ .01 6. multiply both sides by 400 to get 4.9)

p. 60: A college student expects to earn at least $1,000 in interest on an initial investment of $20,000. If the money is invested for one year at an annual interest rate of 'r' percent, compounded quarterly, what is the least annual interest rate that would achieve the goal?

the 2 intersection points can be approximated at (0.78, 0.61) and (-1.28, 1. 64) (1. Set g(x) = f(x) and get x^2 = -1/2x + 1 which equals x^2 + 1/2x - 1 = 0 or 2x^2 + x - 2 = 0 2. Solve the equation 2x^2 + x -2 = 0 for x using the quadratic formula and get x = (-1 ± √1+16)/4. This represents the x-coordinates of the 2 solutions-> x = ((-1 + √17)/4) = 0.78 and x = ((-1 - √17)/4)= -1.28. 3. Square the x-values to get the y-values or do g((-1 + √17)/4)= ((-1 + √17)/4)^2 = 0.61 and g( ((-1 - √17)/4)= ((-1 - √17)/4)^2 = 1.64 4. Thus, the 2 intersection points can be approximated by (0.78, 0.61) and (-1.28, 1.64)

p. 73: The graph of both the linear equation y = -1/2x + 1 and the quadratic equation y = x^2 are shown in Algebra Figure 9. Note that the graphs of 'f' and 'g' in Algebra Figure 9 intersect at 2 points. These are the points at which g(x) = f(x). Find these points algebraically.

a) 2x^2 + 6x + 5 b) 14x + 1 c) x + 4 d) 6x^2 + 13x - 5

p. 80: Simplify each of the following algebraic expressions: a) 3x^2 - 6 + x + 11 - x^2 + 5x b) 3(5x - 1) - x + 4 c) (x^2-16)/(x-4) where x ≠ 4 d) (2x+5)(3x-1)

a) 1 b) -1 c) 2

p. 81, Ex. 4: If the function 'g' is defined for all nonzero numbers 'y' by g(y)=y/|y|, find the value of each of the following: a) g(2) b) g(-2) c) g(2)- g(-2)

a) n^2 b) (st)^7 c) r^8 d) 32a^5/b^5 e) 1/(w^15)

p. 81, ex. 5: Use the rules of exponents to simplify the following: a) (n^5)(n^-3) b)(s^7)(t^7) c) r^12/r^4 d) (2a/b)^5 e) (w^5)^-3

(a)(1/a) = 1

(a)(a^-1) =

x^4 y^15/2

(x^2/3 y^5/4)^6

-factor; multiple; 1 and -1 -multiple; factor; 0

-1 is a --- of every integer; 1 is not a --- of any integer except --- -0 is a --- of every integer; 0 is not a --- of any integer except ---

infinitely many

-the list of positive multiples of 25 has no end: 25, 50, 75, 100...; likewise every nonzero integer has ---- multiples

undefined

0^0 =

b (can do 'guess and check' for each possible answer)

14) Of the 48 pencils in a school supply cabinet, 75% had black lead. An administrator added enough black lead pencils to the cabinet to bring the percentage with black lead up to 80%. How many total pencils were in the cabinet after the additional pencils were added? a) 56 b) 60 c) 64 d) 68 e) 72

25 (part = % x whole)

15 is 60% of what number?

a, c, e (plug and solve; an integer can't have a decimal)

15) Which of the following is a possible value of 'k' for which -24/√k is an integer. Indicate all such values a) 9 b) 12 c) 16 d) 25 e) 64

b

17) In a three-digit number n, the hundreds digit is 3 times the units digit. Quantity A: the units digit of 'n' Quantity B: 4 a) quantity A is greater b) quantity B is greater c) the two quantities are equal d) the relationship cannot be determined from the information given

d

20) Rhonda is 5 times older than Frank is right now. Quantity A: Rhonda's age in 13 years Quantity B: Three times Frank's age in 13 years a) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.

f) d^3 g) x^15/y^6 (1. for x: 10 - (-5) = x^15; for y: -1 - 5 = y^-6 2. y^-6 goes into the denominator to make y positive) h) 9x^2y^3

p. 81, ex. 5: Use the rules of exponents to simplify the following: f) (5^0)(d^3) g) [(x^10)(y^-1)]/[(x^-5)(y^5)] h) (3x/y)^2 / (1/y)^5

d) the 2 solutions are -6 and 1/2 e) the 2 solutions are -7 and 2 f) the 2 solutions are (1 + √5)/2 and (1 - √5)/2

p. 82, ex. 6: Solve for x d) (x+6)(2x-1) = 0 e) x^2 + 5x - 14 = 0 f) x^2 - x - 1 = 0

48 miles per hour and 56 miles per hour (1. x + [x + 8] = 104 (208/2 = 204; divide by 2 bc x and x + 8 represent the cars' hourly rate which is 1 hour instead of 2 2. 2x + 8 = 104 -> x = 48 (rate of slower car) 3. 48 + 8 = 56 (rate of the faster car)) ---OR--- (1. 208-16= 192 (how far the slower car has traveled after 2 hours) -subtract '16' bc 8 x 2 -> bc 208 miles apart after *2* hours and one car travels 8 miles slower than the other 2. 192/2 = 96 -divide by 2 bc 2 different cars 3. 96/2 = 48 -divide by 2 again bc takes place over span of 2 hours 4. 192-48 = 56 miles)

p. 83, Ex. 14: Two cars started from the same point and traveled on a straight course in opposite directions for 2 hours, at which time they were 208 miles apart. If one car traveled, on average, 8 miles per hour faster than the other car, what was the avg speed of each car for the 2-hour trip?

a) $4,320 b) $108 ($4320/40) (Let x equal the fixed total cost Cost per person for 40 people = x/40 Cost per person for 36 people = x/36 Since cost per person for 36 people is greater by $12 , we can set up a equation as: x/36 = x/40 + 12- > x/36 - x/40 = 12 10x - 9x /360 = 12 x = 12 * 360 = 4,320-> Cost per person for 40 people = 4,320 / 40 = 108)

p. 83, Ex. 15: A group can charter a particular aircraft at a fixed total cost. If 36 people charter the aircraft rather than 40 people, then the cost per person is greater by $12. a) What is the fixed total cost to charter the aircraft? b) What is the cost per person if 40 people charter the aircraft?

a) P = cy - x b) Profit per chair: P/c = cy-x/c = y - (x/c)

p. 83, Ex. 16: Antiques dealer bought 'c' antique chairs for a total of 'x' dollars. The dealer sold each chair for 'y' dollars. a) Write an algebraic expression for the profit 'P' earned from buying and selling the chairs b) Write an algebraic expression for the profit per chair

15 to 8 (cross multiply-> set up proportion and do 2 x 4, 5 x 3)

p. 83: Ex. 10- If the ratio of 2x to 5y is 3 to 4, what is the ratio of x to y?

$660 (712.8 x .92)

p. 83: Ex. 11- Kathleen's weekly salary was increased by 8% to $712.80. What was her weekly salary before the increase?

$9

p. 83: Ex. 12- A theater sells children's tickets for half the adult ticket price. If 5 adult tickets and 8 children's tickets cost a total of$81, what is the cost of an adult ticket?

$800 at 10% and $2,200 at 8% (x + y = 30000.1x + 0.08y = 256 Now we'll solve by substitution. Isolate x in the first equation: x = 3000 - y And plug that into the second equation: 0.1(3000 - y) + 0.08y = 256 Multiply: 300 - 0.1y + 0.08y = 256 Add: 300 - 0.02y = 256 Subtract 300: -0.02y = -44 Divide by -0.02: y = 2200 And y is the amount of money invested at 8%. This leaves 800 to be invested at 10%)

p. 83: Ex. 13- Pat invested a total of $3,000. Part of the money was invested in a money market account that paid 10% simple annual interest, and the remainder of the money was invested in a fund that paid 8% simple annual interest. If the total interest earned at the end of the first year from these investments was $256, how much did Pat invest at 10% and how much at 8%?

83 (8 + 3 = 11) (x + x + 5 = 11-> x = 3; 11-3 = 8 -> 2 digits are 8 and 3) (x = y + 5; x + y =11)

p. 83: Ex. 9- For a given 2-digit positive integer, the tens digit is 5 more than the units digit. The sum of the digits is 11. Find the integer

1, 5, 25 and their negatives (5 x 5 = 25; 1 x 5 =25-> these integers multiple together to get a multiple of 25)

the 6 integers that 25 is a multiple of

100% (ex: amount increase/base = 300-150/150 = 100%)

what is the percent increase if a quantity doubles in size

20% (amount decrease/base = 500-400/500 = 100/500 = 20/100 = 20%)

what's the percent decrease if a quantity goes from 500 to 400