Question

8. Nate bought two large pizzas and one small pizza and paid $36. If the difference in cost between a large and small pizza is $5.25, how much does a small pizza cost?

Answer 1

$8.5

Explanation:

We need to propose a system of equations with the information provided to us.

two large pizzas and one small pizza cost $36:

`2L+S=36`

where

`L`: Large pizza

`S:` Small pizza

and the difference in cost between a large and small pizza is $5.25:

`L-S=5.25`

our system of equations is:

`2L+S=36`

`L-S=5.25`

We are asked for the price of small pizza, so we must manipulate the equations in such a way that adding or subtracting them removes the variable L and we are left with an equation for S.

Multiply the second equation of the system by -2

`(-2)(L-S=5.25)\\\\-2L+2S=-10.5`

and now we sum this with the first equation of the system:

`-2L+2S=-10.5\\+(2L+S=36)\\-------------\\-2L+2L+2S+S=-10.5+36`

simplifying the result:

`3S=25.5`

and solving for S (the price of a small pizza)

`S=25.5/3\\S=8.5`