Question 1

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.

Accepted Answer

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 2

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

Accepted Answer

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

Question 3

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.

Accepted Answer

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

Question 4

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-A bank loaned out $63,000, part of it at the rate of 11% per year and the rest at a rate of 4% per year. If the interest received was $4830, how much was loaned at 11%?

Accepted Answer

A)  $33,000 
B)  $29,000 
C)  $30,000 
D)  $34,000

Question 5

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.

Accepted Answer

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

Question 6

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.

Accepted Answer

A)   
B)   
C)   
D)

Question 7

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.

Accepted Answer

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

Question 8

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

Accepted Answer

A)   
B)   
C)   
D)

Question 9

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?

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

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?

Accepted Answer

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

Question 12

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?

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

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.

Accepted Answer

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 16

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-An airplane flies 480 miles with the wind and 320 against the wind in the same length of time. If the speed of the wind is 20 mph, what is the speed of the airplane in still air?

Accepted Answer

A)  90 mph 
B)  40 mph 
C)  100 mph 
D)  105 mph

Question 17

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.)

Accepted Answer

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

Question 18

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-To make each Martini at the Faculty Holiday Party, Prof. Smith mixes 3 ounces of vodka and 1 ounce of dry Vermouth. If the vodka is 28% alcohol by volume and the Vermouth is 11% alcohol by volume, what is the
Percentage of alcohol in each Martini?

Accepted Answer

A)  19.5% 
B)  23.8% 
C)  39% 
D)  9.8%

Question 19

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?

Accepted Answer

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

Question 20

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.

Accepted Answer

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

Exam 3: Applications of Algebra

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

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.

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. -A bank loaned out $63,000, part of it at the rate of 11% per year and the rest at a rate of 4% per year. If the interest received was $4830, how much was loaned at 11%?

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.

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.

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.

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

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

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?

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

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

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.

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. -An airplane flies 480 miles with the wind and 320 against the wind in the same length of time. If the speed of the wind is 20 mph, what is the speed of the airplane in still air?

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.)

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?

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.