Mr. McBride ordered 6 cheese pizzas and 7 pepperoni pizzas and paid $153.50 for his son's birthday party. He realized he was going to run out of pizza and made a second order. This time, he ordered 2 cheese and 2 pepperoni pizzas and paid $47.00. What is the cost of one pepperoni pizza?

The cost of one pepperoni pizza and cheese pizza is $12.50 and $11 respectively

let

cost of each cheese pizza = x

cost of each pepperoni pizza = y

The equation:

6x + 7y = 153.50 (1)

2x + 2y = 47.00 (2)

multiply (2) by 3

6x + 6y = 141 (3)

6x + 7y = 153.50 (1)

subtract (3) from (1)

7y - 6y = 153.50 - 141

y = 12.50

substitute y = 12.50 into (2)

2x + 2y = 47.00 (2)

2x + 2(12.50) = 47

2x + 25 = 47

2x = 47 - 25

2x = 22

x = 22/2

x = 11

Therefore, the cost of one pepperoni pizza and cheese pizza is $12.50 and $11 respectively

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Let x = cost of one cheese pizza.

Let y = cost of one pepperoni pizza.

Set up a system of equations.

6x + 7y = 153.50

2x + 2y = 47.00.

Multiply the second equation by -3

6x + 7y = 153.50

-6x - 6y = -141.00.

Add the equations together

y = $12.00.

Plug 12 into one of our original equations.

2x + 2(12) = 47.

Simplify the left side.

2x + 24 = 47.

Subtract 24 from each side.

2x = 23.

Divide each side by 2

x = $11.50

In conclusion, one pepperoni pizza costs $12.00

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.