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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?
a. admission fee: $3.25 skate rental fee: $2.50
c. admission fee: $3.00 skate rental fee: $2.00
b. admission fee: $3.50 skate rental fee: $3.00
d. admission fee: $4.00 skate rental fee: $3.50

Respuesta :

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.

Answer: The correct answer is choice a.

Explanation:

In solving the equation we will variables a = admission and b = rental fees.

The equations for John and Juanita are as follows:

6a + 5b = $32.00

7a + 5b = $35.25

In order to solve this we will subtract John’s equation from Juanita’s, which will equal:

7a + 5b = $35.25 minus

6a + 5b = $3200

a = $3.25

Now you substitute the value of a into the equation to solve for b:

(6 x 3.25) + 5b = $32.00

19.50 + 5b = 32.00

Subtract 19.50 from each side:

5b = 12.50

Divide both sides by 5:

b = $2.50

Admission Fee (a) = $3.25, Skate Rental Fee (b) = $2.50, which is choice a.

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