Question

(08.06) A school fair ticket costs $8 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who went to the fair was 30, and the total money collected was $100. Which of the following options represents the number of children and the number of adults who attended the fair that day, and the pair of equations that can be solved to find the numbers?

Answer 1

Call the number of adults $a$ and the number of children $c$. We then know:
$a+c=30$
and using the given costs:
$8a+c=100$
thus:
$c=30-a$
$8a+30-a=100$
$7a=70$
$a=10$
by backsubstitution:
$a+c=30$
$10+c=30$
$c=20$

10 Adults and 20 Children