Question

Jack and Jill both ordered pizzas from Wayne’s pizza for their parties. Jack paid $58.50 for 3 pepperoni pizzas and 2 plain pizzas. Jill paid $67 for two pepperoni pizzas and 4 plain pizzas. How much does Wayne’s pizza charge for a plain pizza and for a pepperoni pizza ?

Answer 1

One plain pizza would be $10.50 and one pepperoni pizza would be $12.50.

Answer 2

A plain pizza is $10.50. A pepperoni pizza is $12.50.

Explanation:

Solve a system of equations. Call x the price of plain pizzas and y the price of pepperoni pizzas. From the question we are told that for Jack:

`58.50=2x+3y`

And for Jill:

`67=4x+2y`

There are several ways to solve this. I'll used elimination. Multiply the first equation by 2:

`117=4x+6y`

Now subtract the second equation from the first - this will get rid of the x, leaving only y, which can be solved for:

`(117-67)=(4x-4x)+(6y-2y)\\50=4y\\y=12.5`

Now sub the value for y into either of the original equations and solve for x. I'll use the first:

`58.5=2x+3(12.5)\\58.5=2x+37.5\\21=2x\\x=10.5`