Defining Variables in Word Problems

The Frederick County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride. Which equations could be used to determine how many rides you would need to go on for both fairs to be of equal value?

• 15x + 2.5 = 10x + 3

• 15 - 2.5x = 10 - 3x

• 15 + 2.5x = 10 + 3x

• 15 - 10 = 2.5x + 3x

At Gamestop you can buy a Xbox One for $150.00 and each game to go with it would cost $24.00. Or, you can buy a Playstation 4 for $180.00 and each game for $20.00. Write an equation to determine how many games would need to be purchased for the cost to be equal?

• 150x + 24 = 180 + 20x

• 150 + 24x = 180 + 20x

• 180 - 150 = 24 x + 20x

• 150 - 24x = 180 - 20x

Taxi company A charges $8.00 to get into the cab and $0.75 per mile. Taxi company B charges $6.00 to get into a cab and $1.25 per mile. How many miles would the cost be the same for both companies?

• 2 miles 

• 4 miles

• 0.50 mile

• -4 miles 

Mary has been offered two jobs. Job A has a starting salary of $36,000 and a raise of $1500 every year. Job B has a starting salary of $29,000 and a raise of $2500 every year. In how many years would Mary's salary be the same at both companies. What would that salary be?

• 8 years; $46500

• 7 years; $45600

• 8 years; $45600 

• 7 years; $46500 

At a store a carton of eggs costs $2.25 and a package of bacon costs $4.25. At another store eggs cost $2.75 and bacon costs $4.00. If you were to buy one carton of eggs, how many packages of bacon would you have to buy for both stores to cost the same?

• 2

• 4

• 1

• 6

Which situation best represents the following equation? 25 + .05x = 50 + .01x

• There are two cell phone companies that charge based on the number of minutes used each month, x. Cellular One charges $50 plus 5 cents per minute. Cellular Plus charges $25 plus 1 cent per minute. How many minutes can be used in one month to make the two companies charge the same amount?

• There are two cell phone companies that charge based on the number of minutes used each month, x. Cellular One charges $25 plus $5 per minute. Cellular Plus charges $50 plus $1 per minute. How many minutes can be used in one month to make the two companies charge the same amount?

• There are two cell phone companies that charge based on the number of minutes used each month, x. Cellular One charges $25 plus 5 cents per minute. Cellular Plus charges $50. How many minutes can be used in one month to make the two companies charge the same amount?

• There are two cell phone companies that charge based on the number of minutes used each month, x. Cellular One charges $25 plus 5 cents per minute. Cellular Plus charges $50 plus 1 cent per minute. How many minutes can be used in one month to make the two companies charge the same amount?

John and Jane went to a bakery to get cookies for a party. Jane bought x cookies that were $3 each. John bought x cookies that were on sale for $1 plus he got a small cake for $10.00. If John and Jane both spent the same amount of money, which equation shows how many cookies, x, they purchased.

• 3x = x + 10

• x = 3x + 10

• 3x + x = 10

• 3x + x + 10 = 0

I can join video club A for $25.00 and rent videos for $1.00 each. Or, I can join video club B for $15.00 and rent videos for $2.00 each. If I were to rent 6 videos which club would be the better deal? How much would I spend?

• $25 

• $30

• $25

• $27

Joe’s Canoes charges an initial fee of $20 plus $4 an hour. Callie’s Canoes charges a flat rate of $14 an hour. Find the number of hours for which the total amount that both places charge would be the same.

• 3 hours

• 4 hours

• 1 hour

• 2 hours

Juan decided to join a gym to get in shape for football. He has two payment options. Option A is to buy a membership card and pay $2 each time he goes to the gym. Option B is to pay $4 each time he goes. A membership card costs $30. After how many times, t, will the cost of Option A be equal to the cost of Option B

• 50

• 20

• 15

• 25