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2 years ago

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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 altog

ether 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.

1 answer:

Rama09 [41]2 years ago

5 0

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

$G = 9/1.5$

$G = 6$

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Step-by-step explanation:

First, start by setting up the equation.

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Thanh's equation also has an intial fee and an hourly rate. So, the equation will be

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First, subtract from both sides. We will do the numbers without variables first.

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<em>____________________</em>

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<u>To check your answer, you can plug into the original equation. </u>

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