Question

an amusement park sells adult tickets and child tickets. adult tickets cost more than child tickets. heather purchased 10 tickets for $71 to give to her family. she created the system of equations shown to model this situation.
$12x + 5y = 71$
$x + y = 10$
the solution to heather’s system is $(3, 7)$. which statement correctly interprets this solution?
a each child ticket costs $3 and each adult ticket costs $7.
b heather purchased 3 child tickets and 7 adult tickets.
c heather purchased 7 child tickets and 3 adult tickets.
d each child ticket costs $7 and each adult ticket costs $3.

Explanation:

Step1: Define variables

Let $x$ = number of adult tickets, $y$ = number of child tickets

Step2: Match solution to variables

Solution $(3,7)$ means $x=3$, $y=7$

Step3: Verify cost equation consistency

Check $12x+5y=12(3)+5(7)=36+35=71$, which matches total cost.

Step4: Interpret ticket counts

$x=3$ (adult tickets), $y=7$ (child tickets)

Answer:

B. Heather purchased 3 child tickets and 7 adult tickets.