Math 9

Equations and Inequalities – Word Problems

1.  The slide at Sportsworld charges 75¢ to rent a mat, plus 50¢ for each time you ride the slide. Write an inequation stating that you can afford to pay no more than $8.25. Solve the inequation to find the maximum number of times you can ride the slide.

2.  Joe was saving to buy a bike. One weekend he earned $25, but even with this added to his savings he didn’t have the $150 he needed for the bike. Write an inequation showing what you know about Joe’s savings.

3.  The student council in your school decided to raise money by organizing a concert. The cost of hiring a band and renting equipment is $1000 and the council charges $5 per ticket.

  1. Write an inequation stating that the profit from this dance must be more than $1200.
  2. Solve this inequation to find the smallest number of tickets that must be sold to make a profit of at least $1200.

4.  Samantha earns $300 per week plus a commission of $25 for each painting that she sells.

  1. Write an inequation stating that she wants to earn more than $500 per week.
  2. Solve this inequation to find the smallest number of paintings she has to sell to make at least $500.

5.  The cost of a taxi ride is $1.25/km, plus a fixed cost of $2.75.

  1. Write an inequation stating that you only have $10.00 to spend on a taxi ride.
  2. Solve this inequation to find the farthest distance you can travel by taxi.

6.  One brand of cheese is sold in 250g packages for $1.95. A second brand is sold in 700g packages. At what price will the larger package be more economical than the smaller package?

7.  The cost of a taxi ride depends on a fixed cost, plus the charge per kilometer. Acme Cabco charges any part of a kilometer as a full kilometer.

  1. The fixed cost is $2.50 and the cost per kilometer is $1.20. Let d represent the distance (in whole kilometers) you travel in the taxi. Choose the equation that best represents this situation.
  2. C = 2.5d + 1.2? ii. C = 1.2d – 2.5?

iii. C = 1.2d + 2.5 iv. C = 2.5d – 1.2?

  1. Find the cost of travelling no more than 3km in the taxi, using the equation you selected.
  2. Find the cost of travelling at least 2km; less than 3.5km.
  3. Write an equation showing that you paid $13.30 for a taxi ride. Find the least distance you must have traveled.

8.  A gasoline and oil mixture for a power lawn mower is 500mL of oil to 8 L of gasoline. You have no more than 12 L of gasoline. How much oil should be used?

9.  Water flows over Niagara Falls at the rate of 2.8L/s. At this rate, what is the minimum amount flowing over the falls in one year?

10.  Two people travelling in different cars leave at the same time. One travels due east at 80km/h and the other travels due west at 90km/h. If they leave at 9:00 a.m. what is the earliest time that they will be 594km apart?

11.  A jacket that regularly sells for $150 is on sale for at least 25% off the regular price.

  1. What is the least amount of discount on the jacket?
  2. What is the probable sale price of the jacket?
  3. What is the total cost of the jacket? Remember, GST of 5% is added to the sale price. A provincial tax of 10% is also added to the sale price.