Question

jack and jull both orders pizzas from waynes pizza for their parties jack paid 58.50 for 3 pepporonies and 2 plain pizzas jill paid 67 for 2 pepporonies and 4 plain pizzas how much did they pay for each type of pizza.

Answer 1

First, assign a variable to each unknown value. 

Let:
x = cost of the pepperoni pizza
y = cost of the plain pizza

Next, set up equations based on the word problem. We then have the following equations: 

(1) 3x + 2y = 58.50
(2) 2x + 4y = 67

Equation (1) comes from the statement: "Jack paid 58.50 for 3 pepperonies and 2 plain pizzas". Equation (2), on the other hand, translates the statement: "Jill paid 67 for 2 pepperonies and 4 plain pizzas".

To solve for two unknown variables given two independent equations, eliminate one variable first. That is, multiply equation (1) to -2. 

-2[3x + 2y = 58.50]
-6x -4y = -117

Then add this to equation (2):

-6x -4y = -117
2x + 4y = 67
-------------------
-4x        = -50
x = -50/-4 = 12.5

To solve for y, we use equation (2) and substitute the value of x which has been solved already.

2(12.5) + 4y = 67
y = 10.5

To summarize, they paid $12.50 for the pepperoni pizza while they paid $10.50 for the plain pizza.