Question

A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 7 soft drinks for $45.10. The second group bought 6 slices of pizza and 5 soft drinks for $33.34. How much does one slice of pizza cost?

Answer 1

Answer:

The cost of an slice of pizza is $3.94

Explanation:

Hi, we have to construct 2 equations with the information of the problem, the first one is " 8 slices of pizza and 7 soft drinks for $45.10".

$8P+7D=45.10$

And the second one, when "The second group bought 6 slices of pizza and 5 soft drinks for $33.34" is.

$6P+5D=33.34$

Where: P = pizza slices and D= soft drinks

We need to substract one equation from the other, but firs we need to equal one of the variables. In order to do so, we multiply our first equation by 5 and the second one for 7, therefore we get.

First equation

$40P+35D=225.5$

And the second one:

$42P+35D=233.38$

And now, we substract them and solve.

$40P+35D-(42P+35D)=225.5-233.38$

$40P-42P+35D-35D=-7.88$

$-2P=-7.88$

$P=\frac{-7.88}{-2} =3.94$

The cost of a slide of pizza is $3.94

In case you needed to find the cost of the soft drink, we just substitute P for 3.94 in any of the initial equations, that is:

$8(3.94)+7D=45.1$

$7D=13.58$

$D=1.94$

The cost of a soft drink is $1.94

Best of luck.