Question

An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates. John paid the admission fees for his six nephews and rented five pairs of ice skates. He was charged $32.00. Juanita paid the admission fees for her seven grandchildren and rented five pairs of ice skates. She was charged $35.25. What is the admission fee? What is the rental fee for a pair of skates?

Answer 1

C=price per child
S=price per pair of ice skates

John: 6C + 5S = 32.00
Juanita: 7C + 5S = 35.25

You can subtract one equation from the other to cancel out the S's and determine C:
.... 6C + 5S = 32.00
.. -(7C + 5S = 35.25)
_________________
.... 6C + 5S = 32.00
.. -7C - 5S = -35.25
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-C + 0S = -3.25
..........C=3.25

From this, it is determined that C=3.25. You can use this to determine S, by plugging it into one of the equations:
6C + 5S = 32.00
6(3.25) + 5S = 32.00
19.50 + 5S = 32.00
5S = 32.00 - 19.50
5S = 12.50
S = 12.50/5
S = 2.50

Now, it is determined that S = 2.50. You can verify this by plugging it into the other equation.
7C + 5S = 35.25
7(3.25) + 5S = 35.25
22.75 + 5S = 35.25
5S = 35.25 - 22.75
5S = 12.50
S = 12.50/5
S = 2.50

Again, S = 2.50. Therefore, it is correct.

Answer 2

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Answer 3

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Answer 4

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