Question

Jack paid $13.75 to buy slices 3 of pizza and 4 hot dogs at a concession stand. Sarah paid $9.75 to buy 2 slices of pizza and 3 hot dogs from the same stand. What was the price of a slice of pizza?

Answer 1

$13.75 = 3p + 4d
$9.75 = 2p + 3d

Using 2nd equation, divide all factors by 3 to isolate hot dog price and solve in terms of pizza price:

3.25 = 2/3p + d
3.25 - 2/3p = d

Now substitute for d in the other equation:

$13.75 = 3p + 4(3.25 - 2/3p)

Distribute the 4: 

$13.75 = 3p + 13 - 8/3p

Combine factors of p:

$13.75 = 9/3p - 8/3p + 13
$13.75 = 1/3p + 13

Isolate and solve for p:

$13.75 -13 = 1/3p

0.75= 1/3p

0.75 * 3 = p
2.25 = p

The price of pizza was $2.25 per slice.

Answer 2

The hotdogs cost $1.75, and the pizza cost $2.25.