Tickets for the senior play at the local elementary school cost $3 for children, $5 for students, and $8 for adults. 800 tickets were sold and the total in ticket sales was $4750. The number of adult tickets sold was 50 more than two times the number of children tickets. Find the number of each type of ticket using a system of three equations.

Question

Tickets for the senior play at the local elementary school cost $3 for children, $5 for students, and $8 for adults. 800 tickets were sold and the total in ticket sales was $4750. The number of adult tickets sold was 50 more than two times the number of children tickets.  Find the number of each type of ticket using a system of three equations.

Damon · Answer

a = 50 + 2 c
a + s + c = 800
8 a + 5 s + 3 c = 4750
so
50 + 2 c + s + c = 800
or
s + 3 c = 750 that is just in s and c
then also
8 a + 5 s + 3 c = 4750
8 (50 + 2 c) + 5 s + 3 c = 4750
400 + 16 c + 5 s + 3 c = 4750
5 s + 19 c = 4350 that is also just in s and c

So you have
s + 3 c = 750
5 s + 19 c = 4350
multiply the first equation by 5
5 s + 15 c = 3750
5 s + 19 c = 4350
------------------------- subtract
-4 c = - 600
c = 150
Your turn