Question

Giuseppi's Pizza had orders for $490.00 of pizzas. The prices were $17 for a large pizza, $13 for a medium pizza, and $7 for a small pizza. The number of large pizzas was two less than three times the number of medium pizzas. The number of small pizzas was two more than three times the number of medium pizzas. How many of each size of pizza were ordered?

The number of medium size pizzas is _____.

The number of large pizzas is ____.

The number of small pizzas is _____.

Please explain step by step and how you got to each step.

Answer 1

Let the number of medium size pizzas be X.

This means that the number of large size pizzas will be 3X - 2

This means that the number of small size pizzas will be 3X + 2

So, the below equation can be derived:

Number of large size pizzas x price per pizza + Number of medium size pizzas x price per pizza + Number of small size pizzas x price per pizza = Total value of pizzas

(3X - 2) x $ 17 + X x $ 13 + (3X + 2) x $ 7 = $ 490

51X - $ 34 + 13X + 21X + $ 14 = $ 490

85X - $ 20 = $ 490

X = 6

So, the number of medium size pizzas are 6

So, the number of large size pizzas are as follows:

= 3 x 6 - 2

= 16

So, the number of small size pizzas are as follows:

= 3 x 6 + 2

= 20