560 people went to theater. youth tkts cost $5.75 and adult tkts cost $8.50. total receipts were $3,907.50. how many youth tickets were sold?

Question

need a system of equations

Answer 1

Let's write two equations, one for the number of youth and adult tickets sold, and one for the amount spent on youth and adult tickets. 

560=y+a

 

where y=number of youth tickets and a=number of adult tickets

We can write y in terms of a: y=560-a.

 

$5.75y+$8.50a=$3907.50

We can now substitute y for 560-a into the above equation.

$5.75(560-a)+$8.50a=$3907.50

$3220-$5.75a+$8.50a=$3907.50

$2.75a=$687.50

a=250 tickets. 

 

Since y=560-a, y=560-250=310 tickets.

So there were 310 youth tickets sold.