310 youth tickets were sold
Solution:
Let "a" be the number of youth tickets sold
Let "b" be the number of adult tickets sold
Cost of 1 youth ticket = $ 5.75
Cost of 1 adult ticket = $ 8.50
On Friday afternoon, 560 people went to the local theater for the matinee
Therefore,
a + b = 560 ---------- eqn 1
The theater's sales receipts totaled 3907.50
Therefore, we frame a equation as:
number of youth tickets x Cost of 1 youth ticket + number of adult tickets x Cost of 1 adult ticket = 3907.50
[tex]a \times 5.75 + b \times 8.50 = 3907.50\\\\5.75a + 8.50b = 3907.50 --------- eqn 1[/tex]
From eqn 1,
a = 560 - b --------- eqn 2
Substitute eqn 2 in eqn 1
5.75(560 - b) + 8.50b = 3907.50
3220 - 5.75b + 8.50b = 3907.50
2.75b = 3907.50 - 3220
2.75b = 687.5
Divide both sides of equation by 2.75
b = 250
Substitute b = 250 in eqn 3
a = 560 - 250
a = 310
Thus 310 youth tickets were sold
