PS- Light bulbs

mavesum wrote:A number of light bulbs were purchased to illuminate a gym. However, only 2/3 of them were needed and 160 leftover light bulbs were returned. If only 60% of their cost, or $96, was reimbursed, how much money was spent on illuminating the gym?

In future, please provide the answer choices - you lose a lot of great strategy tips when we don't see them.

We know that $96 represents 60% of the cost of 160 bulbs. We also know that 160 is 1/3 the total number of bulbs purchased; therefore, 320 bulbs were actually used.

If 96 = 3/5(cost of 160), then

cost of 160 = (5/3)96 = 5*32 = $160... in other words, the cost is $1/bulb.

So, we used 320 bulbs, that's $320.

We lost $160 - $96 = $64 on our returns.

Total cost = $320 + $64 = $384

We could have solved more quickly if we recognized that:

Total cost = Cost(160 bulbs) + Cost(160 bulbs) + 40%(cost(160bulbs)) = 240%(cost(160 bulbs))

240%(cost(160 bulbs)) = 4*60%(cost(160 bulbs)) = 4*96 = 384

Lots of other ways we could have played with the fractions as well.

Thanks Stewart

First approach suites me

Here is another approach.

Let x = total # of bulbs.
from the problem x/3 = 160.
so x = 480.
# of bulbs used in the gym = 480 - 160 = 320.

60% of 160 = 96
ie. 60/100 * 160 *c = 96.
So c = 1 ie cost of 1 bulb is $1.


So total money spent on bulbs
= 320 + (160 -96) = 320 + 64 = $384.

I used the same approach as vittalgmat

Its always better to have a simple way, because that'swhat you will never forget even when you are under pressure!!