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

To find the cost of each type of pizza, we can set up a system of equations using the given information and solve it.

Step-by-step explanation:

To determine how much Jack and Jill paid for each type of pizza, we need to set up a system of equations using the given information.

1. Let's assume the cost of a pepperoni pizza is 'P' and the cost of a plain pizza is 'Q'.
2. From the first statement, Jack paid $58.50 for 3 pepperonis and 2 plain pizzas, so we can write the equation: 3P + 2Q = 58.50.
3. From the second statement, Jill paid $67 for 2 pepperonis and 4 plain pizzas, so we can write the equation: 2P + 4Q = 67.
4. Now we can solve this system of equations using substitution or elimination to find the values of 'P' and 'Q', which represent the cost of each type of pizza.

By solving the system of equations, we find that the cost of each pepperoni pizza is $12 and the cost of each plain pizza is $11.

Answer 2

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.