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Fri Jan 27, 2017 9:23 am
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
83% (01:54) correct
17%
(02:30)
wrong
based on 328
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History
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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
Fri Jan 27, 2017 11:30 am
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Bunuel
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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General Discussion
Fri Jan 27, 2017 11:15 am
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Let the # of pounds of Cookies that need to be added be C
Then Total Price = .25xC+.85x25
Total weight = C+25
Price per pound needs to be 0.45
=> (.25xC+.85x25)/(C+25) = 0.45
=> .25C+.85x25 = .45C+.45x25
=> .2C = .4x25 = 10
=> C = 50 pounds
Answer is (D)
Then Total Price = .25xC+.85x25
Total weight = C+25
Price per pound needs to be 0.45
=> (.25xC+.85x25)/(C+25) = 0.45
=> .25C+.85x25 = .45C+.45x25
=> .2C = .4x25 = 10
=> C = 50 pounds
Answer is (D)
