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28 Jan 2017, 07:42
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Graham crackers cost $0.25 per pound and marshmallows cost $0.85 per pound. How many pounds of graham crackers must be added to 25 pounds of marshmallows to arrive at a mixture worth $0.45 a pound?
A. 170
B. 100
C. 60
D. 50
E. 20
A. 170
B. 100
C. 60
D. 50
E. 20
28 Jan 2017, 08:21
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Graham crackers cost $0.25 per pound and marshmallows cost $0.85 per pound. How many pounds of graham crackers must be added to 25 pounds of marshmallows to arrive at a mixture worth $0.45 a pound?
A. 170
B. 100
C. 60
D. 50
E. 20
A. 170
B. 100
C. 60
D. 50
E. 20
We can treat this question as a weighted averages question.
We'll just say that graham crackers cost an AVERAGE of $0.25 per pound and marshmallows cost an AVERAGE of $0.85 per pound
Weighted Averages Formula
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...
For this question, we have: Price per pound of marshmallows and graham crackers combined = (proportion of graham crackers)(price per pound of graham crackers) + (proportion of marshmallows)(price per pound of marshmallows)
If we let G = the number of pounds of graham crackers required, then....
TOTAL weight = 25 + G
So, the PROPORTION of graham crackers = G/(25 + G)
And the PROPORTION of marshmallows = 25/(25 + G)
Now let's plug these values into the formula to get...
$0.45 = [G/(25 + G)][$0.25] + [25/(25 + G)][$0.85]
Eliminate fractions by multiplying both sides by (25 + G) to get: 0.45(25 + G) = 0.25G + (25)(0.85)
Simplify: 11.25 + 0.45G = 0.25G + 21.25
Rearrange: 0.2G = 10
Solve: G = 50
Answer: D
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