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: Interpret the values

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

Step4: Verify cost context

Adult tickets cost more: $12 > 5$, so $x$ links to $12$ (adult price), $y$ links to $5$ (child price), which aligns with $x$ being adult tickets.

Answer:

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