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In a certain store, the regular price of a refrigerator is $600. How much money is saved by buying this refrigerator at 20 percent off the regular price rather than buying it on sale at 10 percent off the regular price with an additional discount of 10 percent off the sale price?

This is what I tried:

  1. 20% of 600 is 120. Subtract 120 from 600 $\to$ \$480
  2. Then 10% off the orignal price again $\to$\$480. Then 10% off the sale: 10% of 480 is 48.
  3. Then subtract 480 from 48 which is 432

But my answer sheet says that isn't right. What did I do wrong here?

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10% of 600 is 60, thus the sale price is 540. Ten percent of 540 is 54, thus the second price is 486$. The insight you should have is that the second 10% also reduce the previous (sale based) reduction. – Hagen von Eitzen Nov 7 '12 at 19:46
There's no need to preface every title with "Confusing". – Austin Mohr Nov 7 '12 at 19:48
up vote 2 down vote accepted

You calculated correctly the savings for the first alternative. If we take $20\%$ off the regular price, we save $120$.

Now we need to make an entirely separate calculation for the second alternative. Take $10\%$ off the regular price. That saves us $60$, and brings us to $540$. Then take $10$ percent off that. That brings us to $540-54=486$. Our total savings are $60+54=114$.

So in the first case we save $120$, in the second case we save $114$, for a difference of $6$ dollars.

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You have:

  1. 20% off of \$600 is \$480
  2. 10% off of \$600 is \$480

Only one of these is right.

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  1. 20% off \$600 gives you \$480.
  2. 10% off the regular price, \$600, gives you a sale price of \$540.
  3. 10% off the sale price gives you 540 - 54 = \$486.

So it's a comparison between \$480 and \$486. You save \$6 with the first option.

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