SOLUTION: A cook used all of a 2-pound chunk of cheese in making three recipes. Recipe I used one-third as much cheese as Recipe II did, and Recipe II used one-half as much cheese as Recipe

Question 484827: A cook used all of a 2-pound chunk of cheese in making three recipes. Recipe I used one-third as much cheese as Recipe II did, and Recipe II used one-half as much cheese as Recipe III.
a. What part of the whole chunk of cheese, and how many pounds, did each recipe use?
b. If the whole chunk of cheese cost $6.60, how much was the cheese in each recipe worth.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
A cook used all of a 2-pound chunk of cheese in making three recipes. Recipe I used one-third as much cheese as Recipe II did, and Recipe II used one-half as much cheese as Recipe III.
a. What part of the whole chunk of cheese, and how many pounds, did each recipe use?
b. If the whole chunk of cheese cost $6.60, how much was the cheese in each recipe worth.
=======================================
a.
Let a = the amount of cheese in recipe I.
Let b = the amount in recipe II.
Then the amount in recipe III = 2 - a - b
Given:
I used 1/3 as much as II.
a = b/3 [1]
II used one-half as much as III.
b = 1/2(2 - a - b) [2]
Use the value for a in [1] into [2]:
b = 1/2(2 - b/3 - b)
b = 1 - b/6 - b/2
b = 1 - b/6 - 3b/6
10b/6 = 1
b = 6/10 = 3/5
Therefore a = 3/15 = 1/5
and recipe III contains 2 - 1/5 - 3/5 = 6/5
So the amounts are 1/5, 3/5 and 6/5 pounds for recipe I, II and III resp.
b.
The cheese costs $6.60/2 lbs = $3.30 per pound
I: 1/5lb*3.30 = $0.66
II: 3/5lb*3.30 = $1.98
III: 6/5lb*6.60 = $3.96
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