SOLUTION: 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?

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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