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A number of light bulbs were purchased to illuminate a gym. However, only \(\frac{2}{3}\) of them were needed and 160 leftover light bulbs were returned. If only 60% percent of their cost, or $96, was reimbursed, how much money was spent on illuminating the gym?

A number of light bulbs were purchased to illuminate a gym. However, only \(\frac{2}{3}\) of them were needed and 160 leftover light bulbs were returned. If only 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

First find the cost of a single light bulb, which is \(\frac{\frac{96}{160}}{60\%}=\frac{6}{10}*\frac{10}{6}=$1\), because only 60% of the cost was reimbursed.

Next find the number of light bulbs that were purchased: \(\frac{160}{1-\frac{2}{3}} = \frac{160}{\frac{1}{3}} = 160*3 = 480\). The number of bulbs that were used is equal to \(480*\frac{2}{3} = 320\). Multiply that number by the cost of a light bulb and add the money which was not reimbursed to find the answer, which is \(320*1 + 160*1*(100\% - 60\%) = 320 + 64 = $384\).

A number of light bulbs were purchased to illuminate a gym. However, only \(\frac{2}{3}\) of them were needed and 160 leftover light bulbs were returned. If only 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

First find the cost of a single light bulb, which is \(\frac{\frac{96}{160}}{60\%}=\frac{6}{10}*\frac{10}{6}=$1\), because only 60% of the cost was reimbursed.

Next find the number of light bulbs that were purchased: \(\frac{160}{1-\frac{2}{3}} = \frac{160}{\frac{1}{3}} = 160*3 = 480\). The number of bulbs that were used is equal to \(480*\frac{2}{3} = 320\). Multiply that number by the cost of a light bulb and add the money which was not reimbursed to find the answer, which is \(320*1 + 160*1*(100\% - 60\%) = 320 + 64 = $384\).

Answer: E

Hi Bunuel

I find the wordings bit confusing

1) If only 60% percent of their cost, or $96, was reimbursed,

So, basically 96 = 60% of Total cost which gives us Total cost = 160

2) Now 160 was the cost for 480 bulbs ,

hence money was spent on illuminating the gym i.e. 320 bulbs = (160 * 320 ) / 480 = 320 / 3 = ~ $ 106

A number of light bulbs were purchased to illuminate a gym. However, only \(\frac{2}{3}\) of them were needed and 160 leftover light bulbs were returned. If only 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

First find the cost of a single light bulb, which is \(\frac{\frac{96}{160}}{60\%}=\frac{6}{10}*\frac{10}{6}=$1\), because only 60% of the cost was reimbursed.

Next find the number of light bulbs that were purchased: \(\frac{160}{1-\frac{2}{3}} = \frac{160}{\frac{1}{3}} = 160*3 = 480\). The number of bulbs that were used is equal to \(480*\frac{2}{3} = 320\). Multiply that number by the cost of a light bulb and add the money which was not reimbursed to find the answer, which is \(320*1 + 160*1*(100\% - 60\%) = 320 + 64 = $384\).

Answer: E

Hi Bunuel

I find the wordings bit confusing

1) If only 60% percent of their cost, or $96, was reimbursed,

So, basically 96 = 60% of Total cost which gives us Total cost = 160

2) Now 160 was the cost for 480 bulbs ,

hence money was spent on illuminating the gym i.e. 320 bulbs = (160 * 320 ) / 480 = 320 / 3 = ~ $ 106

Where am I going wrong ???

Thanks

480 light bulbs purchased. 320 light bulbs used. 160 light bulbs returned. 60% percent of the cost of those 160, or $96, was reimbursed. Thus the cost of 160 light bulbs is $160 out of which 60%, or $96 were reimbursed and the remaining $64 were NOT reimbursed.

The cost of 320 light bulbs is $320, plus $64 that were NOT reimbursed = $384.
_________________

A number of light bulbs were purchased to illuminate a gym. However, only \(\frac{2}{3}\) of them were needed and 160 leftover light bulbs were returned. If only 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

First find the cost of a single light bulb, which is \(\frac{\frac{96}{160}}{60\%}=\frac{6}{10}*\frac{10}{6}=$1\), because only 60% of the cost was reimbursed.

Next find the number of light bulbs that were purchased: \(\frac{160}{1-\frac{2}{3}} = \frac{160}{\frac{1}{3}} = 160*3 = 480\). The number of bulbs that were used is equal to \(480*\frac{2}{3} = 320\). Multiply that number by the cost of a light bulb and add the money which was not reimbursed to find the answer, which is \(320*1 + 160*1*(100\% - 60\%) = 320 + 64 = $384\).

Answer: E

Hi Bunuel

I find the wordings bit confusing

1) If only 60% percent of their cost, or $96, was reimbursed,

So, basically 96 = 60% of Total cost which gives us Total cost = 160

2) Now 160 was the cost for 480 bulbs ,

hence money was spent on illuminating the gym i.e. 320 bulbs = (160 * 320 ) / 480 = 320 / 3 = ~ $ 106

Where am I going wrong ???

Thanks

480 light bulbs purchased. 320 light bulbs used. 160 light bulbs returned. 60% percent of the cost of those 160, or $96, was reimbursed. Thus the cost of 160 light bulbs is $160 out of which 60%, or $96 were reimbursed and the remaining $64 were NOT reimbursed.

The cost of 320 light bulbs is $320, plus $64 that were NOT reimbursed = $384.

Ok Got it !

The highlighted part in yellow confused me initially - but now its clear - cool problem

Instead of that last step of finding the cost of the used bulbs and then adding the cost of the un-reimbursed sum to the total, I saved a bunch of time by just taking the total cost of the bulbs ($480) and subtracting how much was reimbursed ($96 and no math needed, since it was included in the question).

A number of light bulbs were purchased to illuminate a gym. However, only \(\frac{2}{3}\) of them were needed and 160 leftover light bulbs were returned. If only 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

Dear Bunuel,

This is good question. However, the wording is confusing. I did not understand what 'their' refer to. Does it refer to 60% of cost of leftover or to total cost of whole bulbs?

Although I agree with explanation, the wording of the question at best is ambiguous. The "full stop" after "were returned" is doing the damage. I believe the wording of the question can be improved.

"Their cost" doesn't give a clear indication as to what light bulbs is it referring to.

60% of 160 bulbs =96 total cost of 160 bulbs = 96+160*(40/100)=96+64=160 =>1 bulb=1 rupee Total number of bulbs= X total cost => X*1=2/3X*1+160*1=>X=480 96 was reimbursed so 480-96 =384

I still understood the question correctly. For 'verbal-oriented' folks, I can understand how 'their' can hinder their understanding. Maybe if we can say "60% of their cost" -> "60% of the cost" it helps them?