Question

The Barnett triplets went to the school carnival. Henry rode on 5 rides, bought 2 drinks , 1 bag of popcorn and spent $20.50. Mary spent $16.50 on 3 rides, 3 drinks and 1 bag of popcorn. While Tim rode rode on 6 rides only purchased 1 drink and spent $20.00. How much did each ride cost?a: $12b: $3c: $2d: $4

Answer 1

Let:

x = Cost of each ride

y = Cost of each drink

z = Cost of each bag of pocorn

so:

Henry rode on 5 rides, bought 2 drinks , 1 bag of popcorn and spent $20.50:

`5x+2y+z=20.50_{\text{ }}(1)`

Mary spent $16.50 on 3 rides, 3 drinks and 1 bag of popcorn:

`3x+3y+z=16.5_{\text{ }}(2)`

Tim rode rode on 6 rides only purchased 1 drink and spent $20.00:

`6x+y=20_{\text{ }}(3)`

Solve the system:

`\begin{gathered} (1)-(2) \\ 5x-3x+2x-3y+z-z=20.5-16.5 \\ 2x-y=4_{\text{ }}(4) \end{gathered}`
`\begin{gathered} (3)+(4) \\ 6x+2x+y-y=20+4 \\ 8x=24 \\ x=(24)/(8) \\ x=3 \end{gathered}`

Answer:

Each ride cost $3