The Pi (π) Club at Math High School was planning a fundraiser to sell pepperoni pizza. A pizza company donated enough ingredients to make the equivalent of 300 extra large pepperoni pizzas (16” diameter). In trying to determine the number of pizzas of each size to make, they surveyed students in the school. Based on the survey, the club decided that more than half of the pizzas they make should be extra large; there would be more large (14” diameter) than medium (12” diameter) and between 40 and 50 small (10” diameter). The club members plan to sell the pizzas for $11(small), $15 (medium), $18 (large), and $20 (extra-large).

Question

The Pi (π) Club at Math High School was planning a fundraiser to sell pepperoni pizza. A pizza company donated enough ingredients to make the equivalent of 300 extra large pepperoni pizzas (16” diameter). In trying to determine the number of pizzas of each size to make, they surveyed students in the school. Based on the survey, the club decided that more than half of the pizzas they make should be extra large; there would be more large (14” diameter) than medium (12” diameter) and between 40 and 50 small (10” diameter). The club members plan to sell the pizzas for $11(small), $15 (medium), $18 (large), and $20 (extra-large). 
How many pizzas does the club make for each size?

Steve · Answer

If there are w,x,y,z pizzas of the sizes, then we have

100w+144x+196y+256z = 300*256
z >= 150
y > x
40 <= w <= 50

You have said nothing about how much they need to make from the sales, so the price information is just noise.