A skating rink changes one admission price for adults and a different admission price for children. The total admission price for a group of 4 adults and 10 children is $57. The total admission price for a group of 3 adults and 7 children is $41. What are the admission prices for an adult and for a adult?

Given:

The total admission price for a group of 4 adults and 10 children is $57.

The total admission price for a group of 3 adults and 7 children is $41.

To find:

The admission prices for an adult and for a children.

Solution:

Let the price of an adult be x and price of children be y.

According to the question,

        ...(i)

     ...(ii)

Multiply equation (i) by 3.

        ...(iii)

Multiply equation (i) by 4.

     ...(iv)

Subtract (iv) from (iii).

Divide both sides by 2.

Put y=3.5 in (i).

Divide both sides by 4.

Therefore, the price for an adult is $5.5 and price for a child is $3.5.

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step-by-step explanation:

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step-by-step explanation: