Algebra Word Problem

Question

It costs $60 to go to the movies for 2 adults and 5 children. It costs $66 for 5 adults and 2 children. Write a system and solve for the price of an adult and a child’s ticket.

Answer 1

We need to turn this word problem into a system of equations in order to solve it.

Let's call our variables "A" for the price of an adult ticket and "K" for the price of a kid ticket.

1. 2 adults and 5 kids costs $60 so: 2A + 5K = 60
2. 5 adults and 2 kids costs $66 so: 5A + 2K = 66

Then we can solve for A in the first equation:

2A + 5K = 60

2A = 60 - 5K

A = 30 - 5/2K

Then plug that equation into the second equation:

5A + 2K = 66

5 (30 - 5/2K) + 2K = 66

150 - 25/2K + 2K = 66

84 = 10.5K

8 = K

Now that we know the value for K, we can plug it in and solve:

5A + 2K = 66

5A + 2 (8) = 66

5A = 50

A = 10

So the cost of an adult ticket is $10 and the cost of a kids ticket is $8.

I hope this is helpful!