Number of adult tickets sold = 17
Number of student tickets sold =32
Number of senior citizen tickets sold = 51
Solution:
Given that a certain school sells:
adult tickets = $ 8 ; student tickets = $ 5 and senior citizen tickets = $ 6
Let the number of adult tickets sold be "a"
Let the number of student tickets sold be "b"
Let the number of senior citizen tickets sold be "c"
For one game 100 tickets were sold for $ 600
Number of adult tickets sold + number of student tickets sold + number of senior citizen tickets sold = 100
a + b + c = 100 ------ eqn 1
Number of adult tickets sold x price of one adult ticket + number of student tickets sold x price of one student tickets + number of senior citizen tickets sold x price of one senior citizen tickets = 600
8a + 5b + 6c = 600 ----- eqn 2
There are 3 times as many adult tickets sold as senior citizen tickets
Hence we get,
3a = c -------- eqn 3
Put eqn 3 in eqn 1 we get,
a + b + 3a = 100
4a + b = 100
b = 100 - 4a ----- eqn 4
Substitute eqn 3 and eqn 4 in eqn 2, we get
8a + 5(100 - 4a) + 6(3a) = 600
8a + 500 - 20a + 18a = 600
6a = 600 - 500
a = 16.67 that is approximately 17
a = 17
Substitute a = 17 in eqn 3,
3(17) = c
c = 51
Substitute a = 17 in eqn 4,
b = 100 - 4(17) = 100 - 68 = 32
b = 32
Thus we get:
number of adult tickets sold = a = 17
number of student tickets sold = b = 32
number of senior citizen tickets sold = c = 51
