How many pounds of carrots and potatoes does the owner need?

Question

A restaurant owner is buying potatoes and carrots from her vegetable supplier. The supplier will deliver no more than $500 worth of product in each delivery. Each pound of potatoes costs $3.25 and each pound of carrots costs $2.47. The owner needs to buy at least three times as many pounds of potatoes as pounds of carrots. Let p represent the number of pounds of potatoes and let c represent the number of pounds of carrots, where p and c are nonnegative integers.

Answer 1

need 3 times as many potatoes as carrots, so p = 3c

equation for total price of product is 3.25p + 2.47c = 500

substitute p (potato) into equation

3.25(3c) + 2.47 = 500

c = 40.9 lbs

p = 3(40.92) = 122.8 lbs

total pounds of carrots and potatoes = 163.7 lbs