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?

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! :)
a=42, c=21