310 youth tickets were sold
<em><u>Solution:</u></em>
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
<em><u>On Friday afternoon, 560 people went to the local theater for the matinee</u></em>
Therefore,
a + b = 560 ---------- eqn 1
<em><u>The theater's sales receipts totaled 3907.50</u></em>
<em><u>Therefore, we frame a equation as:</u></em>
number of youth tickets x Cost of 1 youth ticket + number of adult tickets x Cost of 1 adult ticket = 3907.50
![a \times 5.75 + b \times 8.50 = 3907.50\\\\5.75a + 8.50b = 3907.50 --------- eqn 1](https://tex.z-dn.net/?f=a%20%5Ctimes%205.75%20%2B%20b%20%5Ctimes%208.50%20%3D%203907.50%5C%5C%5C%5C5.75a%20%2B%208.50b%20%3D%203907.50%20---------%20eqn%201)
<em><u>From eqn 1,</u></em>
a = 560 - b --------- eqn 2
<em><u>Substitute eqn 2 in eqn 1</u></em>
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
<em><u>Substitute b = 250 in eqn 3</u></em>
a = 560 - 250
a = 310
Thus 310 youth tickets were sold