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16 Sep 2014, 00:57
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First-grade tobacco is priced at $30 per kilogram, whereas second-grade tobacco is priced at $20 per kilogram. If a blend consists solely of first and second-grade tobacco, what percentage of the blend must be second-grade tobacco for the overall cost to be $22 per kilogram?
A. 20%
B. 30%
C. 60%
D. 75%
E. 80%
A. 20%
B. 30%
C. 60%
D. 75%
E. 80%
16 Sep 2014, 00:57
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Official Solution:
First-grade tobacco is priced at $30 per kilogram, whereas second-grade tobacco is priced at $20 per kilogram. If a blend consists solely of first and second-grade tobacco, what percentage of the blend must be second-grade tobacco for the overall cost to be $22 per kilogram?
A. 20%
B. 30%
C. 60%
D. 75%
E. 80%
Let \(x\) represent the proportion of second-grade tobacco in the blend. The cost for a kilogram of the blend can be calculated as \(20x + 30(1 - x) = 22\). From this, we deduce that \(x = 0.8\), or 80%.
Answer: E
First-grade tobacco is priced at $30 per kilogram, whereas second-grade tobacco is priced at $20 per kilogram. If a blend consists solely of first and second-grade tobacco, what percentage of the blend must be second-grade tobacco for the overall cost to be $22 per kilogram?
A. 20%
B. 30%
C. 60%
D. 75%
E. 80%
Let \(x\) represent the proportion of second-grade tobacco in the blend. The cost for a kilogram of the blend can be calculated as \(20x + 30(1 - x) = 22\). From this, we deduce that \(x = 0.8\), or 80%.
Answer: E
JackSparr0w
GMAT 1: 650 Q39 V41
Posts: 168
03 Nov 2014, 19:24
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See page 57 in the Manhattan statistics book....
No formulas needed. Look at the mix. It has a cost of $22. What is the differential for the First grade tobacco? +$8. What is the differential for the Second Grade Tobacco? -$2.
In order to get the +8 and -2 to cancel out, we'd need to multiply the -2 by 4.
Ex: (1)(8) - (4)(-2) = 0
Therefore, the ratio of the Second grade to First grade is 4:1
So for every 4 parts second grade there is 1 part first grade.
The question asks for the percentage of second grade in the blend. Well we know the blend has 4 parts second and 1 part first grade, so 5 parts total. We also know that second grade is 4 of the total 5 parts. So, 4/(4+1) or 4/5 = 8/10 = 80%
No formulas needed. Look at the mix. It has a cost of $22. What is the differential for the First grade tobacco? +$8. What is the differential for the Second Grade Tobacco? -$2.
In order to get the +8 and -2 to cancel out, we'd need to multiply the -2 by 4.
Ex: (1)(8) - (4)(-2) = 0
Therefore, the ratio of the Second grade to First grade is 4:1
So for every 4 parts second grade there is 1 part first grade.
The question asks for the percentage of second grade in the blend. Well we know the blend has 4 parts second and 1 part first grade, so 5 parts total. We also know that second grade is 4 of the total 5 parts. So, 4/(4+1) or 4/5 = 8/10 = 80%
