Question

1 Admission to the local movie theater is $3 for each child and $7 for each adult. A group of 12 people pay $64 admission. How many children are in this group?

Answer 1

Given:

Admission to the local movie theater is $3 for each child and $7 for each adult.

A group of 12 people pay $64 admission.

To find:

The number of children in a group.

Solution:

Let the number of children be x and number of adults be y.

According to the question,

Total persons : $x+y=12$          ...(i)

Total cost : $3x+7y=64$     ...(ii)

Multiply equation (i) by 7 and subtract the result from (ii).

$3x+7y-7(x+y)=64-7(12)$

$3x+7y-7x-7y=64-84$

$-4x=-20$

Divide both sides by -4.

$x=5$

Therefore, the number of children is 5.