Question

Grace is going to a carnival that has games and rides. Each game costs $1.50 and each ride costs $2.50. Grace spent $16.50 altogether at the carnival and the number of games she played is twice the number of rides she went on. Write a system of equations that could be used to determine the number of games Grace played and the number of rides Grace went on.

Answer 1

Number of Rides:
`5.5R = 16.5`

Number of Games:
`1.5G = 9`

Explanation:

Given

Represent the games with G and the Rides with R

`G = 1.50` -- cost

`R = 2.50` --- cost

`Total = 16.50` -- cost

Required

Represent the system using an equation

The equation can be represented as follows;

`G + R = Total`

Assume She plays G games and had R rides, we have

`1.5G + 2.5R = 16.5`

Since she plays twice as much games as rides,

This implies;

`G = 2R`

So, we have

`1.5 * 2R + 2.5R = 16.5`

`3R + 2.5R = 16.5`

`5.5R = 16.5` --- This equation can be used to solve for Number of Rides

Solving further

`R =16.5/5.5`

`R =3`

Substitute 3 for R in
`1.5G + 2.5R = 16.5`

`1.5G + 2.5 * 3 = 16.5`

`1.5G + 7.5 = 16.5`

Solve for 1.5G

`1.5G = 16.5 - 7.5`

`1.5G = 9` --- This equation can be used to solve for Number of Games

Solving further

`G = 9/1.5`

`G = 6`