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23 Jan 2008, 08:46
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E
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Difficulty:
55%
(hard)
Question Stats:
68% (02:08) correct
32%
(02:23)
wrong
based on 152
sessions
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A number of light bulbs were purchased to illuminate a gym. However, only \(\normal\frac{2}{3}\) of them were needed. The extra 160 light bulbs were returned. 60% percent of their cost, or $96, was reimbursed. How much money was spent on illuminating the gym?
A. $160
B. $320
C. $360
D. $372
E. $384
A. $160
B. $320
C. $360
D. $372
E. $384
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11 Oct 2024, 15:02
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Official Solution:
A gym purchased a certain number of light bulbs to illuminate the space but it turned out that only 2/3 of the bulbs were needed, so 160 bulbs were returned. If the returned light bulbs were reimbursed at 60% of their cost, resulting in a reimbursement of $96, what was the total amount of money spent on lighting the gym?
A. $160
B. $320
C. $360
D. $372
E. $384
Assume the cost of one light bulb to be \($x\). Since \($96\) is 60% of the cost of 160 light bulbs, then the full cost of 160 bulbs can be determined by solving the equation \(160*x*0.6=96\), which gives \(x=$1\)
Next, since only 2/3 of the light bulbs were kept, 160 bulbs that were returned constitute 1/3 of the initial order. Therefore, the total number of bulbs purchased was 480. The initial cost of the order would be \($480\). However, \($96\) was reimbursed for the returned bulbs, resulting in a final cost of the order equal to \(480 - 96=$384\).
Answer: E
A gym purchased a certain number of light bulbs to illuminate the space but it turned out that only 2/3 of the bulbs were needed, so 160 bulbs were returned. If the returned light bulbs were reimbursed at 60% of their cost, resulting in a reimbursement of $96, what was the total amount of money spent on lighting the gym?
A. $160
B. $320
C. $360
D. $372
E. $384
Assume the cost of one light bulb to be \($x\). Since \($96\) is 60% of the cost of 160 light bulbs, then the full cost of 160 bulbs can be determined by solving the equation \(160*x*0.6=96\), which gives \(x=$1\)
Next, since only 2/3 of the light bulbs were kept, 160 bulbs that were returned constitute 1/3 of the initial order. Therefore, the total number of bulbs purchased was 480. The initial cost of the order would be \($480\). However, \($96\) was reimbursed for the returned bulbs, resulting in a final cost of the order equal to \(480 - 96=$384\).
Answer: E
General Discussion
23 Jan 2008, 08:57
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C
x - money that was spent on illuminating the gym.
\((x+96)*\frac13*\frac{60}{100}=96\)
\(x=5*96-96=4*96=384\)
I think it is easy-medium level. But maybe I have wrong answer?
x - money that was spent on illuminating the gym.
\((x+96)*\frac13*\frac{60}{100}=96\)
\(x=5*96-96=4*96=384\)
I think it is easy-medium level. But maybe I have wrong answer?
