Quote:
A number of light bulbs were purchased to illuminate a gym. However, only 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?
Total nr of bulbs bought initially - say
nOf these bulbs,
2/3 of them were used and hence 1/3 (1-2/3) bulbs were returned to the retailer.
This implies that
1/3 (of) n bulbs were returned.
1/3 of n = 160 bulbs ==>
n = 480 (Remember n refers to the original nr and 160 refers to the number of bulbs
that were returned)
Lets determine the nr of bulbs that were used for
lighting the gym. 2/3 of (480) = 320 bulbs were used to illuminate the gym.
Ok, now comes the tricky part. As per the question stem -
60% of the their cost was refunded.The trick is to understand
identify the antecedent of the pronoun "their"
This interpretation makes sense.
Think of if this way, some retailers sell products under the condition that on return, they will
NOT refund 100 % of the amount paid by the customer.Instead they will refunded a reduced % - say 70 % of the initial price. This policy is to discourage people from buying large quantities and then return these products for a refund.
Back to the question :-
When 160 bulbs were returned, the retailer refunded only 60% of the COST of THESE 160 bulbsi.e .6x of (total cost of 160 bulbs that were returned) = $96
total cost of 160 bulbs that were returned = $160
Cost of 1 bulb = $1
Total Cost of lights used to decorate the gym= Cost of the 320 Bulbs that were not returned = 320 x $1
= $320