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

Answer:

Number of Rides:     $5.5R = 16.5$  

Number of Games:    $1.5G = 9$

Step-by-step 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

$G = 9/1.5$

$G = 6$