## Problema Solution

A pizza shop delivered 17 pepperoni pizzas to a College on the first night of final exams. The total cost of the pizzas was $145. A small pizza cost three dollars and contains 2 ounces of pepperoni a medium pizza cost seven dollars and contains 9 ounces of pepperoni a large pizza cost $14 and contains 13 ounces of pepperoni. The owner of the pizza shop use 9 lbs. 5 oz. of pepperoni and making the 17 pizzas how many pizzas of each size were delivered to the college.

## Answer provided by our tutors

Let

S = the number of small pizzas that costs $3 and has 2 oz of pepperoni

M = the number of medium pizzas that costs $7 has 9 oz of pepperoni

L = the number of large pizzas that costs $14 has 13 oz pepperoni

The total number of pizzas deilvered is 17 means:

S + M + L = 17

The total cost is $145 means:

3S + 7M + 14L = 145

The owner of the pizza shop use 9 lbs. 5 oz in total means:

2S + 9M + 13L = 149 (since 9 lbs. 5 oz converted to oz is 9*16 + 5 = 149 oz (since 1 lbs = 16 oz)

We need to solve the following system of equations:

S + M + L = 17

3S + 7M + 14L = 145

2S + 9M + 13L = 149

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S = 4 small pizzas

M = 7 medium pizzas

L = 6 large pizzas

There were 4 small, 7 medium and 6 large pizzas delivered.