Question

Daniel Capo

Solve System of Equations from Context
Jan 21,7:26:04 PM
Sydney is going to a carnival that has games and rides. Each game costs $1.25 and
each ride costs $2.25. Sydney spent $24.25 altogether at the carnival and the number
of rides she went on is 3 more than the number of games she played. Determine the
number of games Sydney played and the number of rides Sydney went on.
Sydney played
games and went on
rides rides.
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Answer 1

The number of games Sydney played is 5 and the number of rides she went on is 8.

Explanation:

Given:

Sydney is going to a carnival that has games and rides. Each game costs $1.25 and each ride costs $2.25. Sydney spent $24.25 altogether at the carnival and the number of rides she went on is 3 more than the number of games she played.

Now, to find the number of games Sydney played and the number of rides she went on.

Let the number of games she played be
`x.`

As given, the number of rides she went on is 3 more than the number of games she played.

So, the number of rides be
`x+3.`

Each game costs $1.25 and each ride costs $2.25. Sydney spent $24.25 altogether at the carnival.

According to question:

`1.25x+2.25(x+3)=24.25`

`1.25x+2.25x+6.75=24.25`

`3.50x+6.75=24.25`

Subtracting both sides by 6.75 we get:

`3.50x=17.50`

Dividing both sides by 3.50 we get:

`x=5.`

Number of games = 5.

So, number of rides:

`x+3\\=5+3\\=8.`

Therefore, the number of games Sydney played is 5 and the number of rides she went on is 8.