Completing the exercises here is your opportunity to learn by applying the concepts we just discussed.
IMPORTANT
For each question, set up your equations by carefully reading the text of the question:
- define the meaning of two variables (write “let” statements)
- create two equations
Then check whether your “set up” is correct using these partial solutions:
After that, solve the linear system you came up with. Verify whether your algebra is correct using a left-side/right-side check. Only when needed, consult the full solutions:
Make a real effort to complete each question before opening its answer.
TIP
If you would rather work from paper, use the Print button on this page, or open the handout directly:
Question 1
At a sale in a retro music store, all CDs are one price and all tapes are another price. Three CDs and two tapes cost $72. One CD and three tapes cost $52. What are the prices of one CD and one tape?
Answer
One CD costs $16 and one tape costs $12.
Question 2
A sports club charges an initiation fee and a monthly fee. At the end of 5 months, a member had paid a total of $170. At the end of 10 months, she had paid a total of $295. What was the initiation fee?
Answer
The initiation fee is $45. (The monthly fee is $25.)
Question 3
A tennis club charges an annual fee and an hourly fee for court time. One year, one member played for 39 hours and paid $384. Another member played for 51 hours and paid $456. Determine the annual fee and the hourly fee.
Answer
The annual fee is $150 and the hourly fee is $6.
Question 4
Three footballs and one soccer ball cost $155. Two footballs and three soccer balls cost $220. Determine the cost of one football and the cost of one soccer ball.
Answer
One football costs $35 and one soccer ball costs $50.
Question 5
For the school play, one adult ticket cost $5.00 and one student ticket cost $3.00. Twice as many student tickets as adult tickets were sold. The total receipts were $1650. How many of each kind of ticket were sold?
Answer
150 adult tickets and 300 student tickets were sold.
Question 6
An American football stadium has 20Â 000 seats between the goal lines and 5000 in the end zones. An end-zone seat is $5 cheaper than one between the goal lines. For one game, the revenue was $350Â 000 when all seats were sold. What is the cost of each type of seat?
Answer
A seat between the goal lines costs $15 and an end-zone seat costs $10.
Question 7
When 20 bolts are placed in a box, the total mass is 340 g. When there are 48 bolts in the box, the total mass is 760 g. Determine the mass of the box and the mass of each bolt.
Answer
The box has a mass of 40 g and each bolt has a mass of 15 g.
Question 8
A crate of 36 grapefruit has a total mass of 4 kg. When 12 grapefruit are removed, the total mass is 3 kg. Determine the mass of the crate and the mass of one grapefruit.
Answer
The crate has a mass of 1 kg and one grapefruit has a mass of kg, or about 0.083 kg (83 g).
Curriculum connection
B1.2
solve problems that arise from realistic situations described in words or represented by linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method (Sample problem: The Robotics Club raised $5000 to build a robot for a future competition. The club invested part of the money in an account that paid 4% annual interest, and the rest in a government bond that paid 3.5% simple interest per year. After one year, the club earned a total of $190 in interest. How much was invested at each rate? Verify your result.).
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