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 6 nephews and rented five pairs of ice skates.

He was charged $32. Juanita paid admission fees for her seven grandchildren and rented 5 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

if we let admission fee per child to be a and the rental fee for the skates to be s.

Then john 6a + 5s =32

Juanita 7a + 5s = 35.25

Solving simultaneously we can eliminate s to solve for a first by subtracting one equation from the other.

6a + 5s = 32

7a + 5s = 35.25

we get -a + 0s = -3.25 therefore a= 3.25

Then we can solve for s by substituting a in either of the two equations

6 (3.25) + 5s =32

19.5 + 5s =32

5s = 12.5

s = 12.5/5

s = 2.5

Therefore, the admission fee: $ 3.25 per person and rental fee: $ 2.5 per pair of skates.

Explanation: