Deck 3: Applications of Algebra

Question 1

Express the statement as an algebraic expression.
A number increased by 102

A) 102
B) x + 102
C) 102x
D) x - 102

Answer 1

x + 102

Question 2

Express the statement as an algebraic expression.
26 less than a number

A) 26x
B) x + 26
C) x - 26
D) 26 - x

Answer 2

x - 26

Question 3

Select a variable to represent one quantity and state what that variable represents. Express the second quantity in terms of
the variable selected.
Last year, Rebecca received a grant of g dollars for school. This year she received $5000 plus seven-eighths of last year's amount.

A) + 5000g = new grant amount
B) + 5000 = new grant amount
C) + g = old grant amount, then g = new grant amount
D) = old grant amount, then g = new grant amount

Answer 3

+ 5000 = new grant amount

Question 4

Write the indicated expression.
Kim had a baby weighing x pounds and y ounces. Write an expression that represents the baby's weight in ounces.

A)
B) 16x + y
C)
D) 16(x + y)

Question 5

Determine what x =.
Kathryn is 5 centimeters shorter than Amir.

A) x = Kathryn's height
B) x = Amir's height plus Kathryn's height
C) x = Amir's height
D) x = Kathryn's height minus Amir's height

Question 6

Express the statement as an algebraic expression.
Sam Roberts used to type p words per minute. After taking an advanced typing course, his speed increased by 50 words per minute. Write an expression that represents his new typing speed.

A) 50p + p
B) p + 50
C) 50p
D)

Question 7

Select a variable to represent one quantity and state what that variable represents. Express the second quantity in terms of
the variable selected.
The average time it takes to get through a check-out line at a large wholesale club is 12 minutes more than 4 times the time it takes to get through a check-out line at a small grocery store, s.

A) let s = time at small store, then 12s + 4 = time at large club
B) let s = time at small store, then 12·4 + s = time at large club
C) let s = time at small store, then (12 + 4)s = time at large club
D) let s = time at small store, then 4s + 12 = time at large club

Question 8

Express the statement as an algebraic expression.
The sum of twice a number and 48

A) 96 + x
B) 2x + 48
C) 2(x + 48)
D) 2 + x + 48

Question 9

Determine what x =.
The motorcycle costs $13,000 more than the moped.

A) x = cost of the motorcycle minus the cost of the moped
B) x = cost of the moped
C) x = cost of the motorcycle
D) x = cost of the moped plus the cost of the motorcycle

Question 10

Determine what x =.
Ryan has 67 plastic blocks that are either yellow or green.

A) x = number of yellow blocks or x = number of green blocks
B) x = number of green blocks
C) x = number of yellow blocks plus number of green blocks
D) x = number of yellow blocks

Question 11

Express the statement as an algebraic expression.
14 less than the product of 9 and a number

A) 9 + x - 14
B) 9x - 14
C) 14 - 9x
D)

Question 12

Express the statement as an algebraic expression.
Alexander is t years old. Write an expression that represents Chandler's age if he is 4 times as old as Alexander.

A) 4t + t
B) 4 + t
C) 4t
D)

Question 13

Express the statement as an algebraic expression.
One-fourth the weight , w, increased by 8 pounds

A)
B)
C)
D)

Question 14

Express the statement as an algebraic expression.
One-sixth the height , f

A)
B) 6f
C)
D)

Question 15

Express the statement as an algebraic expression.
Two kilometers less than the distance, d

A)
B)
C)
D)

Question 16

Express the statement as an algebraic expression.
Five times the difference of a number and 20

A) 5x - 20
B)
C) 5(x - 20)
D) 5(20 - x)

Question 17

Determine what x =.
Kristian received 575 more than twice times the number of miles than Louis did on their plane trips to California.

A) x = number of miles that Louis received
B) x = number of miles that Kristian received
C) x = number of miles that Kristian received or x = number of miles that Kristian received
D) x = number of miles that Kristian and Louis received

Question 18

Express the statement as an algebraic expression.
The sum of a 76 and a number

A) 76x
B) 76 - x
C) 76 + x
D) 76

Question 19

Express the statement as an algebraic expression.
Twice the sum of a number and 5

A) 2(x + 5)
B) 10 + x
C) 5(x + 2)
D) 2x + 5

Question 20

Express the statement as an algebraic expression.
The quotient of a number and 94

A)
B) 94x
C) 94 - x
D)

Question 21

Write an equation to represent the problem.
Michele has a dollhouse, (which is an exact replica of her "real" house), in which the size of the dollhouse is 1 th the size of her "real" house. The difference between the length of a side of her "real" house and the length
16
Of a side of her dollhouse is 96 feet.

A)
B) = 0
C) = 96
D) = 96

Question 22

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
The sum of a number and 2 is 7.

A) x - 2 = 7; 9
B) x + 2 = 7; 5
C) x ÷ 2 = 7; 14
D)

Question 23

Write an equation to represent the problem.
The difference of twice a number and 10 is 14.

A) 2x + 10 = 14
B) x - 2 ·10 = 14
C) 10 - 2x = 14
D) 2x - 10 = 14

Question 24

Write an equation to represent the problem.
Markus Lawson is 4 years older than three times Pam Lincoln's age. The sum of their ages is 73. Let a represent Pam's age.

A) a + (3a - 4) = 73
B) a + (3a + 4) = 73
C) a - (3a + 4) = 73
D) a + (a + 34) = 73

Question 25

Write an equation to represent the problem.
Jennifer Park's 2007 income was 6.9% greater than her 2006 income. Her income in 2007 was $78,100. Let i represent 2006 income.

A) i - 0.069i = 78,100
B) 2i + 0.069i = 78,100
C) i + 0.069·78,100 = 78,100
D) i + 0.069i = 78,100

Question 26

Write the indicated expression.
Kevin and Amir share in the profits of a pet supplies store. If the total profit is $80,000 and p is the amount of profit Keven receives, write an expression for the amount Amir receives.

A) p - $80,000
B) p + $80,000
C) $80,000 - p
D) $80,000 + p

Question 27

Write the indicated expression.
The smaller of two numbers is 52 less than four times the larger number. Write an expression for the smaller number subtracted from the larger number. Let n represent the larger number.

A) 4n - (n - 52)
B) n - (n - 4·52)
C) n - (4n - 4·52)
D) n - (4n - 52)

Question 28

Write the indicated expression.
The price of Investor Growth mutual fund is 23% greater than the price of Investor Value mutual fund. Write an expression for the sum of Growth and Values mutual funds. Let n represent the Investor Value.

A) 2n + (n + 0.23n)
B) n + (n + 0.23n)
C) n + 0.23n
D) n + (n - 0.23n)

Question 29

Write an equation to represent the problem.
Lauren Wolf purchased a dress at a 20% off sale. She paid $114 for the dress. Let p represent the price of the dress.

A) p - 0.2 = 114
B) p - 0.2p = 114
C) 0.2p - p = 114
D) p + 0.2p = 114

Question 30

Write an equation to represent the problem.
The sum of a number and 7 is 16.

A) x - 7 = 16
B) 7x = 16
C) x + 7 = 16
D) x ÷ 7 = 16

Question 31

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
At the beginning of the year, the odometer on an SUV read 37,532 miles. At the end of the year, it read 52,412 miles. If the car averaged 24 miles per gallon, how many gallons of gasoline did it use during the year?

A) 14,880 gallons
B) 357,120 gallons
C) 620 gallons
D) 62 gallons

Question 32

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
Andrea decided to rollerblade to her mother's house. Five blocks from her home, one of the wheels on her skate broke, and she had to walk the remaining six blocks to her mother's. She could not repair her skate and had to
Walk all the way back home. How many more blocks did Andrea walk than she skated?

A) 11 blocks
B) 12 blocks
C) 17 blocks
D) 22 blocks

Question 33

Write an equation to represent the problem.
Scot and Elizabeth ate dinner at an upscale bistro. The cost of their meals plus a 16% tip was $63.52.

A) x + 1.6x = 63.52
B) x + 16x = 63.52
C) x + 0.16x = 63.52
D) x + 0.16 = 63.52

Question 34

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
The difference of twice a number and 10 is 20.

A) x - 2 ·10 = 20; 40
B) 10 - 2x = 20; - 5
C) 2x - 10 = 20; 15
D) 2x + 10 = 20; 5

Question 35

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
City A has an elevation of 15,574 feet above sea level while city B has an elevation of 18,476 feet below sea level. How much higher is City A than City B?

A) 2902 ft.
B) 34,150 ft.
C) 34,050 ft.
D) 3002 ft.

Question 36

Write an equation to represent the problem.
Six more than seven times a number is that number increased by 36.

A) 7(x + 6) = x + 36
B) 7x + 6 = 36x
C) 7x - 6 = x + 36
D) 7x + 6 = x + 36

Question 37

Write an equation to represent the problem.
Six times a number is 13 more than two times that number.

A) 6 + x = 2x + 13
B) 6x = 2x + 13
C) 6x + 13 = 2x
D) 6x = 2(x + 13)

Question 38

Write the indicated expression.
The assessed value of Linda Grill's house is 2000 more than twice that of Mel Murphy's house. Write an expression for the sum of the assessed values. Let v represent the value of Mel Murphy's house.

A) v + (2v + 2000)
B) v + (v + 2·2000)
C) v + (v + 2000)
D) v + (2v - 2000)

Question 39

Write the indicated expression.
Keerti found that he had y dimes in his pocket. Write an expression that represents this quantity of money in cents.

A) y + 10
B)
C)
D) 10y

Question 40

Write the indicated expression.
A slice of pie has 200 calories and a scoop of ice cream has 200 calories. If John has x pieces of pie with 3 scoops of ice cream each, write an expression that represents the number of calories he will consume.

A) 3x + 200 + 200
B) 200·3x + 200
C) 200x + 3·200
D) (200 + 3·200)x

Question 41

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
Inclusive of a 7.5% sales tax, a diamond ring sold for $2042.50. Find the price of the ring before the tax was added. (Round to the nearest cent, if necessary.)

A) $1889.31
B) $1900
C) $2195.69
D) $153.19

Question 42

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
During an intramural basketball game, Team A scored 16 fewer points than Team B. Together, both teams scored a total of 150 points. How many points did Team A score during the game?

A) 68 points
B) 83 points
C) 67 points
D) 75 points

Question 43

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
A train ticket in a certain city is $1.50. People who use the train also have the option of purchasing a frequent rider pass for $18.00 each month. With the pass, each ticket costs only $0.75. Determine the number of times in a
Month the train must be used so that the total monthly cost without the pass is the same as the total monthly
Cost with the pass.

A) 25 times
B) 26 times
C) 23 times
D) 24 times

Question 44

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
Ming got a 19% raise in her salary from last year. This year she is earning $226,100. How much did she make last year?

A) $190,000
B) $4,295,900
C) $36,100
D) $11,900

Question 45

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
A couch sells for $1280. Instead of paying the total amount at the time of purchase, the same couch can be bought by paying $300 down and $90 a month for 12 months. How much is saved by paying the total amount at
The time of purchase?

A) $10
B) $200
C) $100
D) $1090

Question 46

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
Megan is having her yard landscaped. She obtained an estimate from two landscaping companies. Company A gave an estimate of $190 for materials and equipment rental plus $55 per hour for labor. Company B gave and
Estimate of $260 for materials and equipment rental plus $45 per hour for labor. Determine how many hours of
Labor will be required for the two companies to cost the same.

A) 6 hours
B) 10 hours
C) 11 hours
D) 7 hours

Question 47

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
Seven more than five times a number is that number increased by 35.

A)
B)
C) 5x + 7 = x + 35; 7
D)

Question 48

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
You inherit $10,000 with the stipulation that for the first year the money must be invested in two stocks paying 6% and 11% annual interest, respectively. How much should be invested at each rate if the total interest earned
For the year is to be $700?

A) $2000 invested at 6%; $8000 invested at 11%
B) $8000 invested at 6%; $2000 invested at 11%
C) $7000 invested at 6%; $3000 invested at 11%
D) $9000 invested at 6%; $1000 invested at 11%

Question 49

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
A car rental agency advertised renting a luxury, full-size car for $29.95 per day and $0.19 per mile. If you rent this car for 3 days, how many whole miles can you drive if you only have $200 to spend.

A) 66
B) 8
C) 879
D) 579

Question 50

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
Mary and her brother John collect foreign coins. Mary has four times the number of coins that John has. Together they have 175 foreign coins. Find how many coins Mary has.

A) 35 coins
B) 140 coins
C) 133 coins
D) 28 coins

Question 51

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
Seven times a number is 18 more than three times that number.

A)
B)
C)
D)

Question 52

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
A promotional deal for long distance phone service charges a $15 basic fee plus $0.05 per minute for all calls. If Joe's phone bill was $62 under this promotional deal, how many minutes of phone calls did he make? Round to
The nearest integer, if necessary.

A) 940
B) 2
C) 9
D) 1540

Question 53

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
A 12-ft. board is cut into 2 pieces so that one piece is 4 feet longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.

A) shorter piece: 6 ft; longer piece: 36 ft
B) shorter piece: 2 ft; longer piece: 10 ft
C) shorter piece: 12 ft; longer piece: 40 ft
D) shorter piece: 32 ft; longer piece: 36 ft

Question 54

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
An accountant receives a salary of $270,775 per year. During the year, he plans to spend $97,000 on his mortgage, $52,000 on food, $39,000 on clothing, $45,000 on household expenses, and $29,000 on other expenses.
With the money that is left, he expects to buy as many shares of stock at $225 per share as possible. How many
Shares will he be able to buy?

A) 36 shares
B) 41 shares
C) 39 shares
D) 38 shares

Question 55

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
When Milo got promoted at work, he received a 10% pay raise. He now earns $33,000 per year. What was his annual salary before his raise?

A) $33,000
B) $3300
C) $30,000
D) $3000

Question 56

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
An auto repair shop charged a customer $417 to repair a car. The bill listed $57 for parts and the remainder for labor. If the cost of labor is $45 per hour, how many hours of labor did it take to repair the car?

A) 7 hours
B) 8.5 hours
C) 9 hours
D) 8 hours

Question 57

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
Center City East Parking Garage has a capacity of 251 cars more than Center City West Parking Garage. If the combined capacity for the two garages is 1227 cars, find the capacity for each garage.

A) Center City East:749 cars
B) Center City East:739 cars Center City West: 478 cars Center City West: 488 cars
C) Center City East:478 cars
D) Center City East:488 cars Center City West: 749 cars Center City West: 739 cars

Question 58

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
After a 14% price reduction, a boat sold for $21,500. What was the boat's price before the reduction? (Round to the nearest cent, if necessary.)

A) $3010.00
B) $25,000
C) $153,571.43
D) $24,510.00

Question 59

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
A car rental agency charges $200 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $425?

A) 875 miles
B) 306.25 miles
C) 900 miles
D) 1700 miles

Question 60

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
You inherit $70,000 from a very wealthy grandparent, with the stipulation that for the first year, the money must be invested in two stocks paying 4% and 10% annual interest, respectively. How much should be invested
At each rate if the total interest earned for the year is to be $4000?

A) $40,000 invested at 4%; $30,000 invested at 10%
B) $50,000 invested at 4%; $20,000 invested at 10%
C) $20,000 invested at 4%; $50,000 invested at 10%
D) $30,000 invested at 4%; $40,000 invested at 10%

Question 61

Solve the problem.
Angle A and angle B are supplementary angles and angle A is 15° less than four times angle B. Find the measures of angle A and angle B.

A) A = 147°, B = 33°
B) A = 125°, B = 55°
C) A = 141°, B = 39°
D) A = 156°, B = 24°

Question 62

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
On a road trip, five friends drove at 50 miles per hour to California. On the way home, they took the same route but drove 75 miles per hour. How many miles did they drive on the way to California if the round trip took 10
Hours?

A) 600 miles
B) 6 miles
C) 1500 miles
D) 300 miles

Question 63

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
Melita Zuba made a $600,000 cash contribution to two charities, the American Brain Tumor Association and the National Brain Tumor Foundation. The amount received by the National Brain Tumor Foundation was 20%
Greater than the amount received by the American Brain Tumor Association. How much did the American
Brain Tumor Association receive?

A) $327,272.73
B) $600,000
C) $272,727.27
D) $500,000.00

Question 64

Solve the problem.
In a parallelogram, each of the two larger angles is 30° less than twice the smaller angles. Find the measure of each angle.

A) smaller angles = 50°; larger angles = 130°
B) smaller angles = 70°; larger angles = 110°
C) smaller angles = 10°; larger angles = 170°
D) smaller angles = 52.5°; larger angles = 127.5°

Question 65

Solve the problem.
A bookcase is to be constructed with three shelves as shown. The height of the bookcase is 6 feet longer than the length of a shelf, and only 30 feet of lumber is available. What should be the width and height of the bookcase?

A) length = 3 feet; height = 18 feet
B) length = 4.5 feet; height = 10.5 feet
C) length = 3 feet; height = 9 feet
D) length = 12 feet; height = 13.5 feet

Question 66

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
Because the budget cutbacks, MaryAnn was required to take a 19% pay cut. If she earned $51,000 before the pay cut, find her salary after the pay cut.

A) $50,903.10
B) $41,310
C) $4131
D) $50,031

Question 67

Solve the problem.
In an isosceles triangle, one angle is 33° greater than the other two angles. Find the measure of all three angles.

A) 57°, 57°, 66°
B) 36.8°, 36.8°, 106.5°
C) 49°, 49°, 82°
D) 33°, 33°, 114°

Question 68

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
Khang and Hector live 45.9 miles apart. They decide to bicycle towards each other and meet somewhere in between. Hector's rate of speed is 70% of Khang's. They start out at the same time and meet 3 hours later. Find
Hector's rate of speed.

A) 6.3 mph
B) 27 mph
C) 9 mph
D) 45.9 mph

Question 69

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
Doreen and Irena plan to leave their houses at the same time, roller blade towards each other, and meet for lunch after 3 hours on the road. Doreen can maintain a speed of 4.8 miles per hour, which is 40% of Irena's
Speed. If they meet exactly as planned, what is the distance between their houses?

A) 50.4 miles
B) 36 miles
C) 20.16 miles
D) 14.4 miles

Question 70

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
Alexander and Judy are 26 miles apart on a calm lake paddling toward each other. Alexander paddles at 3 miles per hour, while Judy paddles at 6 miles per hour. How long will it take them to meet?

A) 8.7 hours
B) 2.9 hours
C) 17 hours
D) 2.8 hours

Question 71

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
Train A leaves a station traveling at 32 km/h. Two hours later, train B leaves the same station traveling in the same direction at 52 km/h. How long does it takes train B to catch up to train A?

A) 3.2 hours
B) 4.2 hours
C) 5.2 hours
D) 2.2 hours

Question 72

Solve the problem.
The perimeter of a rectangular room is 174 feet. Find the length and width of the room if the length is 9 feet longer than twice the width.

A) w = 31 ft; l = 71 ft
B) w = 52 ft; l = 122 ft
C) w = 26 ft; l = 61 ft
D) w = 39 ft; l = 48 ft

Question 73

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
A motorcycle traveling at 60 miles per hour overtakes a car traveling at 30 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles?

A) 60 miles
B) 6 miles
C) 180 miles
D) 3 miles

Question 74

Solve the problem.
The measure of one angle of a quadrilateral is three times the smallest angle; the third angle is 12° greater than the smallest angle; and the fourth angle is 70° less than twice the second angle.

A) angle 1 = 46.4°; angle 2 = 139.3°; angle 3 = 151.3°; angle 4 = 22.9°
B) angle 1 = 52.3°; angle 2 = 104.5°; angle 3 = 64.3°; angle 4 = 139°
C) angle 1 = 59.7°; angle 2 = 179.1°; angle 3 = 71.7°; angle 4 = 49.4°
D) angle 1 = 38°; angle 2 = 114°; angle 3 = 50°; angle 4 = 158°

Question 75

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
Linda and Dave leave simultaneously from the same starting point biking in opposite directions. Linda bikes at 5 miles per hour and Dave bikes at 10 miles per hour. How long will it be until they are 29 miles apart from
Each other?

A) 1.9 hours
B) 5.8 hours
C) 0.5 hours
D) 0.6 hours

Question 76

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
Jeff starts driving at 55 miles per hour from the same point that Lauren starts driving at 40 miles per hour. They drive in opposite directions, and Lauren has a half-hour head start. How long will they be able to talk on their
Cell phones that have a 290-mile range?

A) 3 hours
B) 3.1 hours
C) 3.3 hours
D) 2.8 hours

Question 77

Solve the problem.
Angle A and angle B are complementary angles and angle A is 10° more than three times angle B. Find the measures of angle A and angle B.

A) A = 20°, B = 70°
B) A = 30°, B = 60°
C) A = 60°, B = 30°
D) A = 70°, B = 20°

Question 78

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
The local clothing store marks up the price that it pays to the clothing manufacturer by 30%. If the selling price of a pair of jeans is $105, how much did the clothing store pay for the jeans?

A) $150.00
B) $26.25
C) $136.50
D) $80.77

Question 79

Solve the problem.
A rectangular horse pen is to be fenced and divided into five partitions as shown. The length of the fenced-in area is to be twice the width, and the total amount of fencing to be used is 390 feet. Find the length and width of
The fenced-in area.

A) l = 78 ft, w = 39 ft
B) l = 41 ft, w = 39 ft
C) l = 27.9 ft, w = 14 ft
D) l = 86.7 ft, w = 43.3 ft

Question 80

Solve the problem.

A) 48°
B) 21.2°
C) 157°
D) 138°