PROBLEM
word problem!
A movie theater sells tickets for $8.00 for adults and $6.00 for children. One evening the theater took in $3580 in revenue and sold 525 tickets. How many adults tickets and children tickets were sold?
SOLUTION
Let a equal number of adult tickets and c equal the number of children tickets.
Set up two equations: equation 1 represents the number of tickets sold, equation 2 represents the revenue.
EQUATION 1: a + c = 525
EQUATION 2: 8a + 6c = 3580
Rearrange EQUATION 1 to either solve for a or c. Therefore, c = 525 - a
Substitute the expression for c into EQUATION 2 and solve for a.
EQUATION 2: 8a + 6(525 - a) = 3580
8a + 3390 - 6a = 3580
2a = 190
a = 95
Substitute value for a into EQUATION 1
EQUATION 1: 95 + c = 525
c = 525 - 95
c = 430
Therefore, 95 adult tickets and 430 children tickets were sold.
