Question

8 slices of pizza and 5 sodas cost $36.50. 4 Slices of pizza and 10 sodas cost $37. How much does a slice of pizza cost? How much does a soda cost?
PLEASE HELP

Answer 1

Step-by-step explanation: If we use the variable p to represent our pizzas and s to represent our sodas, if our first equation states than 8 slices of pizza and 5 sodas cost $36.50, that's 8p + 5s = 3650.

Notice that I expressed cost in terms of cents so

that we can avoid having to deal with decimals.

In our second equation, 4 slices of pizza and

10 sodas cost $37, that's 4p + 10s = 3700.

Now let's rewrite our two equations on top of one another.

8p + 5s = 3650

4p + 10s = 3700

To solve this system of equations, I would use addition.

I would multiply the bottom equation by -2

to create a situation where our p's will cancel.

When we do that, we get -8p - 20s = -7400.

Now rewrite the equations once again ~

8p + 5s = 3650

-8p - 20s = -7400

Now add the equations together.

So we have -15s = -3,750.

Divide both sides by -15 and s = 250.

Remember that I expressed cost in terms of cents so

since s = 250, it really means that a soda is $2.50.

Now just plug an s back in for the s in one equation.

When we do this, we find that p = 300.

So a pizza is $3.00