Question

A school luncheon made $630. Adult tickets cost $11 each and child tickets cost eight dollars each. The number of children was half the number of adults. How many of each ticket were sold?

Answer 1

Hello! Lets first start with defining our variables:
a = adult tickets
c = child tickets
Now let’s set up a system of equations:
11a + 8c = 630
c = 1/2a (this can be confusing to some people but the CHILDREN TICKETS = HALF THE ADULT TICKETS)
Ok now we have to solve this:
11a + 8c = 630
c= 1/2a [you can solve this system of equations using substitution!]
11a + 8(1/2a) = 630
11a + 4a = 630
15a = 630
a = 42 (now we know our a value and we can plug that in to find c!)
c = 1/2a
c = 1/2(42)
c = 21
you can check this by plugging in your c and a value into both equations! I hope this helps! :)
Answer: a=42, c=21