Question

Write and solve the system of equations below. Let a represent adults and let c represent children.





1,200 tickets were sold to the spring carnival. Adult tickets cost $6.00 and children's tickets cost $3.50. A total of $6,450 was collected. How many tickets of each kind were sold?

Answer 1

a + c = 1200 ---> a = 1200 - c
6a + 3.5c = 6450

now sub 1200 - c in for a in the other equation
6(1200 - c) + 3.5c = 6450 -- distribute through the parenthesis
7200 - 6c + 3.5c = 6450 -- subtract 7200 from both sides
-6c + 3.5c = 6450 - 7200 -- combine like terms
-2.5c = -750 -- divide by -2.5
c = 300

a + c = 1200
a + 300 = 1200
a = 1200 - 300
a = 900

check..
6a + 3.5c = 6450
6(900) + 3.5(300) = 6450
5400 + 1050 = 6450
6450 = 6450 (correct)

adult tickets sold (a) = 900
child tickets sold (c) = 300