Equation and Inequality Word Problems

Solve the following inequality:
-4x + 14 ≤ 54

• x ≥ -10

• x ≤ -10

• x ≥ 10

• x ≤ 10

Look at the Inequality
Which of the following scenarios could be used to represent it?

• The student council is ordering T-shirts from a website.  The T-shirts cost $9 each and there is a shipping fee of $8 for any amount ordered.  The student council wants to spend no more than $80 on the T-shirts.  What are the possible number of T-shirts they can order?

• The student council is ordering T-shirts from a website.  The T-shirts cost $9 each and there is a shipping fee of $8 for any amount ordered.  The student council wants to spend more than $80 on the T-shirts.  What are the possible number of T-shirts they can order?

• The student council is ordering T-shirts from a website.  The T-shirts cost $9 each and there is a shipping fee of $8 for any amount ordered.  The student council wants to spend less than $80 on the T-shirts.  What are the possible number of T-shirts they can order?

• The student council is ordering T-shirts from a website.  The T-shirts cost $9 each and there is a shipping fee of $8 for any amount ordered.  The student council wants to spend exactly $80 on the T-shirts.  What are the possible number of T-shirts they can order?  

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

Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.65 per mile.  Katie has no more than $10 to spend on the taxi ride.

• 1.75 + 0.65m < 10

• 1.75 + 0.65m > 10

• 1.75m + 0.65 < 10

• 1.75m + 0.65 > 10

Peppy Pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $21 plus $1 per hour. For how many hours is the total fee charged by the companies the same?

• 2 hours

• 3 hours

• 4 hours

• 5 hours

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

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 

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

Renting games online from Netwii costs $3.33 per game  with no monthly fee.  Renting games online from HDO costs $2.00 per game plus a monthly fee of $10.00.
Which inequality represents the situation when the monthly cost at Netwii is more than the monthly cost at HDO?

• 3.33v > 2v + 10

• 3.33v + 10 > 2v 

• 3.33v < 2v + 10

• 3.33v + 10 < 2v