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16 Sep 2014, 00:23
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If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $66, how much does one shirt cost?
A. $10
B. $12
C. $13.20
D. $15
E. $16.80
A. $10
B. $12
C. $13.20
D. $15
E. $16.80
16 Sep 2014, 00:23
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Official Solution:
If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $66, how much does one shirt cost?
A. $10
B. $12
C. $13.20
D. $15
E. $16.80
Let the price of one shirt be \(s\) and that of jeans be \(j\). From the given information, we have the following equations:
\(3j + 2s = 69\)
\(2j + 3s = 66\)
Multiplying the first equation by 2 and the second equation by 3 we get
\(6j + 4s = 138\)
\(6j + 9s = 198\)
Subtracting the first equation from the second, we get: \(5s = 60\), which gives \(s=12\).
Answer: B
If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $66, how much does one shirt cost?
A. $10
B. $12
C. $13.20
D. $15
E. $16.80
Let the price of one shirt be \(s\) and that of jeans be \(j\). From the given information, we have the following equations:
\(3j + 2s = 69\)
\(2j + 3s = 66\)
Multiplying the first equation by 2 and the second equation by 3 we get
\(6j + 4s = 138\)
\(6j + 9s = 198\)
Subtracting the first equation from the second, we get: \(5s = 60\), which gives \(s=12\).
Answer: B
26 Apr 2020, 09:03
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Bunuel
An alternative approach: Using mental math, simply test for equivalence in price for the other item--jeans--after assuming a price for shirts. If the numbers match, you have the answer; if not, you know you need to adjust. Since starting in the middle makes more sense than testing either the highest or lowest values, I would look for the easiest point of entry among the middle three choices: 12 or 15 would do just fine. For the sake of illustration, say you chose 15:
3 jeans + 2($15) = $69, so 3 jeans = $39, or 1 pair of jeans = $13
2 jeans + 3($15) = $66, so 2 jeans = $21, or 1 pair of jeans = $10.50 or, simply, NOT $13
I did not actually work out the $10.50 above because I knew the jeans had to cost less than $13, meaning that I needed to adjust the price of the shirts down for the cost of the jeans to go up. That is, it does not make sense to test $16.80, since the price discrepancy in jeans from one equation to the next would only increase. Eliminate (D) and (E) and repeat the process from before, using the number in the middle of the remaining three answer choices--either it will be the answer itself, or it will point to the correct answer, since we will know whether we need to adjust up or down.
3 jeans + 2($12) = $69, so 3 jeans = $45, or 1 pair of jeans = $15
2 jeans + 3($12) = $66, so 2 jeans = $30, or 1 pair of jeans = $15
The answers match, so (B) must be correct. This approach may look like more trouble than it is worth, but I have only typed out each step of a mental process that takes seconds. The solution can be worked out in half a minute or less without writing anything down, and knowing you are correct, that feeling of certainty, can give you a leg up on the next, maybe tougher, question.
Good luck with your studies.
- Andrew
