Adult tickets to a play cost $22, tickets for children cost $15. 11 people cost $228. Write a system equation for how many adults and children were in the group

Question

Adult tickets to a play cost $22. Tickets for children cost $15. Tickets for a group of 11 people cost $228. Write and alive a system of equations to find how many children and how many adults were in the group.

Answer 1

Here's what we know:

a + c = 11

22a + 15c = 228

 

By moving either a or c over in our first equation, we can create a substitution problem:

c = 11 - a

22a + 15(11 - a) = 228

22a + 165 - 15a = 228

7a +165 = 228

7a = 63

a = 9

So 9 adults.

 

c = 11 - a

c = 11 - 9

c = 2

And 2 children

 

Now to check our answer:

22 * 9 + 2 * 15 = 228

198 + 30 = 228

228 = 228