Question

Stella is going to a carnival that has games and rides. Each game costs $2.50 and each ride costs $4. Stella spent $52.50 altogether at the carnival and the number of rides she went on is twice the number of games she played. Write a system of equations that could be used to determine the number of games Stella played and the number of rides Stella went on. Define the variables that you use to write the system.

Answer 1

• g = number of games
• r = number of rides
• 2.50g +4.00r = 52.50
• r = 2g

Explanation:

You want a system of equations describing Stella's cost of going to the carnival, where she spent $2.50 on each game, and $4 on each ride for a total of $52.50. The number of rides is twice the number of games.

Variable definitions

It is often convenient to use mnemonic variable names, so we choose ...

g = the number of games Stella played

r = the number of rides Stella went on

System of equations

The total cost of tickets is ...

2.50g +4.00r = 52.50

The relation of numbers of games and rides is ...

r = 2g

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Additional comment

It is convenient to substitute for r in the first equation to give ...

2.50g +4.00(2g) = 52.50

10.50g = 52.50 . . . . . . . . . simplify

g = 5 . . . . . . . . . . . . . . divide by 10.50; games Stella played

r = 2(5) = 10 . . . . . . the number of rides Stella went on