Billy went to the Show and spent $78 on a combined total of 9 items including rides and showbags. If each showbag cost $12 and each ride cost $7, how many of each did Billy buy?

First, set x for showbags and y for rides.

So now we need to make a system equations.

Since he bought 9 items, x+y=9.

And because he spent $78 and we know the price of each item, the second equation is 12x+7y=78.

Now solve for the system of equations by elimination.

12x+7y=78

-7 (x+y=9)

Now the new equations are:

12x+7y=78

-7x-7y=-63

Now just subtract.

5x=15

x=3.

And since originally we made x represent showbags, he bought 3 showbags. Which means he bought 6 rides because 9-3=6.

If you wanna check your answer, just plug in.

x+y=9

3+6=9

12 (3) + 6 (7) = 78

36+42=78

Answer: Billy bought 3 showbags and 6 rides.