A pizza shop delivered 17 pepperoni pizzas to a college on the first night of final exams. The total cost of the pizzas was &153. A small pizza cost four dollars and contains 3 ounces of pepperoni. A medium pizza cost six dollars and contains 9 ounces of pepperoni. A large pizza cost $15 and contains 14 ounces of pepperoni. The owner of the Pizza shop used 9 pounds in 8 ounces of pepperoni in making the 17 pizzas. How many pieces of each size were delivered to college?

Step-by-step explanation:

Let x = number of small pizzas

Let y = number of medium pizzas

Let z = number of large pizzas

Total weight of pizza = 9 *16 +8 = 152

Total pizza  = 17

Total amount = $153

x + y + z = 17                     - equation 1

4x + 6y + 15z = 153          - equation 2

3x + 9y + 14z =  152             - equation 3

from equation 1,  x = 17 -y -z - equation *

substitute in both 2 and 3

4(17 -y -z) + 6y + 15z = 153   1

3(17 -y -z) +9y +14z  = 152   --- 2

68 - 4y - 4z +6y + 15z = 153 i

51 - 3y - 3z + 9y + 14z = 152 ---ii

2y + 11z  = 85  ---1

6y +11z = 101  2

equation 2 minus equation 1

4y = 16 => y = 4

substitute y in equation 1

8 + 11z = 85 => 11z = 77 => z = 7

subtitute y as 4 and z as 7 in equation *

x = 17 - 4 -7  => x = 6

So, 6 small pizzas, 4 medium and 7 big pizzas were delivered

3

step-by-step explanation: