an amusement park sells adult tickets and child tickets. adult tickets cost more than child tickets. heather…

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. \n$12x + 5y = 71$\n$x + y = 10$\nthe solution to heather’s system is $(3, 7)$. which statement correctly interprets this solution?\na each child ticket costs $3 and each adult ticket costs $7.\nb heather purchased 3 child tickets and 7 adult tickets.\nc heather purchased 7 child tickets and 3 adult tickets.\nd each child ticket costs $7 and each adult ticket costs $3.

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. \n$12x + 5y = 71$\n$x + y = 10$\nthe solution to heather’s system is $(3, 7)$. which statement correctly interprets this solution?\na each child ticket costs $3 and each adult ticket costs $7.\nb heather purchased 3 child tickets and 7 adult tickets.\nc heather purchased 7 child tickets and 3 adult tickets.\nd each child ticket costs $7 and each adult ticket costs $3.

Answer

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.