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

A rental car agency charges $30.00 per day plus per mile $0.15. Another rental car agency charges $36.00 per day plus $0.10 per mile. How many miles would have to be driven in one day for both rental agencies to cost the same amount to rent? 

• 120 miles
• 100 miles
• 110 miles
• 150 miles 

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

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? 

• A; $25 
• A; $30
• B; $25
• B; $27

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
• .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 

Carol wants to join a dance studio. Studio A charges $100.00 for the entry fee and $45.00 per class, while Studio B charges $125.00 for the entry fee and $30.00 per class. If Carol were to take 5 classes which studio should Carol join? How much would she save joining the cheaper dance studio? 

• Studio A; $40.00
• Studio A; $50.00
• Studio B; $50.00
• Studio B; $40.00 

Blind company A charges $25.00 to install blinds for one room and $5.00 for each additional window. Blind company B charges $30.00 to install blinds in one room and $4.00 for each additional window. Which company is more expensive if I need 6 additional windows installed? How much more expensive would it be? 

• Company A; $1.00
• Company A; $1.25 
• Company B; $1.00 
• Company B; $1.25 

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?