Question

Students sold 390 tickets for a fundraiser at school.

Some tickets are for children and cost $2, while the
rest are adult tickets that cost $5. If the total value of
all tickets sold was $1,470, how many of each type of
ticket was sold?

Answer 1

a = number of adult tix = 230
c = number of child tix = 160

a + c = 390 for number of tickets sold
5a + 2c = 1470 for money earned

First we’ll solve for c in terms of a
c = 390-a

Then we’ll substitute that expression in to solve for a numerical value for c:

5a + 2c = 1470
5a + 2(390 - a) = 1470
5a + 780 -2a = 1470
3a = 690
a = 230

Then we’ll drop that into the first equation to get a numerical value for c

c = 390 - a
c = 390 - 230
c = 160

Check the math:
5a + 2c = 1470
5(230) + 2(160) =
1150 + 320 = 1470