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Question 1108473: Three energy saving improvements are advertised to save 25%, 55% and 20%. A homeowner makes these three improvements in succession. What overall percentabe saving can be expected?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the first improvement saves you 25% of the cost.
your second improvement saves you an additional 55% of the cost after the first improvement.
your third improvement saves you an additional 20% of the cost after the second improvement.
the costs starts with x.
after the first improvement, the cost is x - .25 * x = .75 * x.
after the second improvement, the cost is .75 * x - .55 * .75 * x = .3375 * x.
after the third improvement, the cost is .3375 * x - .20 * .3375 * x = .27 * x.
you went from x to .27 * x.
this is a reduction in cost of .73 = 73%.
that's your overall savings percent.
to see how this works assume the original cost was 1,000.
take off 25% from that to get a first improvement cost of 750.
take off 55% from that to get a second improvement cost of 337.50.
take off 20% from that to get a third improvement cost of 270.
your cost went from 1,000 to 270.
that's a reduction in cost of 730.
the reduction percent is 730 / 1000 = .75 = 73%.
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