Question

A pizzeria sells three sizes of pizza: small, medium, and large. The pizzas sell for $9, $13, and $15, respectively. One evening they sold 28 pizzas and received $320. If they sold 9 more small than large pizzas, how many of each size did they sell?

Answer 1

The solution involves setting up a system of equations to represent the number of small, medium, and large pizzas sold and their respective prices. By substituting expressions, the system can be reduced to two equations with two unknowns. Solving these gives the quantities sold for each pizza size.

Step-by-step explanation:

Let's denote the number of small, medium, and large pizzas as S, M, and L respectively. Given that the sum of the pizzas sold is 28 and the total received is $320, we have:

• S + M + L = 28
• 9S + 13M + 15L = $320

Furthermore, we are told they sold 9 more small pizzas (S) than large pizzas (L), which gives us the equation:

• S = L + 9

To solve for the quantities, we need to solve the system of three equations:

1. S + M + L = 28
2. 9S + 13M + 15L = 320
3. S = L + 9

Using equation (3), we can replace S in equations (1) and (2), giving us two equations with two unknowns, M and L:

1. M + 2L = 19 (after substituting S in equation 1)
2. 13M + 24L = 233 (after substituting S in equation 2)

Solving these simultaneously will give us the values for M and L, and then, using equation (3), we can find S.

Answer 2

Step-by-step explanation:

so if you find the quadratic formula of 3 and multiply it by 82 you get 16. Then if you add 16 and 9 you get 25 this means that they sold 67 large pizzas. Your welcome