Question

Piper and her friend Hunter are going to a carnival that has games and rides. Piper played 5 games and went on 7 rides and spent a total of $43.75. Hunter played 10 games and went on 2 rides and spent a total of $27.50. Determine the cost of each game and the cost of each ride.

Answer 1

• game: $1.75
• ride: $5.00

Explanation:

You want to know the cost of each game and each ride if 5 games and 7 rides cost $43.75 while 10 games and 2 rides cost $27.50.

Setup

We can let g and r represent the cost of a game and the cost of a ride, respectively. Then the two purchases can be described by ...

5g +7r = 43.75

10g +2r = 27.50

Solution

A system of linear equations like this is easily solved by reducing the augmented matrix of coefficients to row-echelon form. Many calculators and web tools are available for the purpose. The attachment shows the result of using a calculator app.

It tells us the price of a game is $1.75, and the price of a ride is $5.00.

Elimination

Using the elimination method of solving the system we can eliminate 'g' by subtracting the second equation from twice the first:

2(5g +7r) -(10g +2r) = 2(43.75) -(27.50)

12r = 60 . . . . . . . simplify

r = 5 . . . . . . . . . divide by 12

10g +2(5) =27.50 . . . . . substitute for r in the second equation

10g = 17.50 . . . . . . . . . subtract 10

g = 1.75 . . . . . . . . . . . divide by 10

The cost of each game is $1.75; the cost of each ride is $5.00.