System of Inequalities word problem

Question

Simon is having a pie eating contest. He wants to buy at least 3 times as many apple pieces as pumpkin pies. Pumkin pies are $3 each and the apple pies are $2 each. He wants to spend at most $36.

Answer 1

Let a = number of apple pies

Let p = number of pumpkin pies

 

a ≥ 3p

2a + 3p ≤ 36

 

If a=3p then

2(3p) + 3p = 36

9p = 36

p = 4  pumpkin pies

a = 12 apple pies

 

Check:

2a + 3p ≤ 36

2(12) + 3(4) = $36

This is the maximum.