Problema Solution
On the opening night of a play at a local theatre, 973 tickets were sold for a total of $11,451. Adult tickets cost $15 each. Children's tickets cost $11 each, and senior citizen tickets $7 each. If the combined number of children and adult tickets exceed twice the number of senior citizen tickets by 169, then how many tickets of each type were sold?
Answer provided by our tutors
Let
a = the number of adult tickets sold, a>=0
c = the number of children's tickets sold, c>=0
s = the number of senior citizen tickets sold, s>=0
Assuming that each person bought one ticket we have:
a + c + s = 973
The total money collected from 973 tickets is #11,451:
15a + 11c + 7s = 11451
The number of adult and children tickets together exceeds 2 times the number of senior citizen tickets by 169:
a + c = 2s + 169
We have the following system of equations:
a + c + s = 973
15a + 11c + 7s = 11451
a + c = 2s + 169
........
click here to see the system of equations solved for a, c and s
........
a = 455 adult tickets
c = 250 children tickets
s = 268 senior citizen tickets
There were 455 adult, 250 children and 268 senior citizen tickets sold.