a ticket booth sold 456 tickets and collected $2311.50 in ticket sales. Adult tickets are $6.50 and child tickets are $2. how many tickets of each type were sole?

Answer 1

I'll try to help.
You know that a certain number of child tickets and a certain number of adult tickets must add up to equal 456.
Say x = adult tickets (number)
y = # child tickets

So x + y = 456
And the money collected is :
6.5x + 2y = 2311.5

2(x + y = 456) ==> 2x + 2y = 912.
6.5x + 2y = 2311.5
- (2x + 2y = 912)
4.5x = 1399.5
x = 1339.5 / 4.5 = 311

311 + y = 456
y = 145
SO # adult tickets = 311 # child tickets = 145
Hope that helped. Peace out.

Answer 2

Adult tickets --->
children tickets --> 456-x

6.5x + 2(456-x) = 2311.5
times 2
13x + 4(456-x) = 4623
9x = 2799
x = 311

so 311 adult tickets and 145 children tickets