Question

A diet food company is attempting to create a non-carb brownie composed entirely of fat and protein. The brownie must weigh at least 10 grams but no more than 100 calories. Fat has 9 calories per gram and protein has 4 calories per gram. Write and graph a system of inequalities that represents weight, in grams, of protein and fat.

Answer 1

The system of inequalities is given by

i) x + y ≥ 10

ii) 9x + 4y ≤ 100

Explanation:

i) let x be the number of grams of fat in the non-carb brownie.

ii) let y be the number of grams of protein in the non-carb brownie.

iii) The brownie must weigh at least 10 grams

iv) therefore we can write x + y ≥ 10

v) The brownie must have no more than 100 calories

vi) therefore we can write 9x + 4y ≤ 100