Brain Teaser - Can you find an explanation as simple as the answer.

It is getting warm and school is almost out and nobody wants to think too hard about math, so here is one with a simple answer. All you have to do is find an explanation that is equally simple.

You go to purchase something that costs so many dollars and so many cents. Suppose that you have enough money in coins to cover the cents part. How much more money in coins will you end up with if you pay only with paper than if you use the coins to to cover the cents part of the price?

Once you figure out what I am talking about, you will see by an example or two that the answer is very easy to express. An easy answer should have an easy explanation. Your challenge is to some up with an explanation understandable by someone who knows no algebra.

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You will end up with a dollar’s worth of change.

Let’s say the item costs \$1.10. You therefore have 10 cents. When you pay with \$2.00 you will get 90 cents back. 90+10=100.

If it cost \$1.35 you would have .35 and get.65 back- \$1.00 again.

When you pay, the storekeeper gives you back the fraction of a dollar that equals \$1.00 minus what you already have. That plus what you have will always equal \$1.00.

crisw (14116)

Not bad, but there is a more compact explanation.

The remainder of coins required to reach the nearest dollar. Your change.

Consider a side by side comparison of the total amount of paper money that you end up with in the two cases and bear in mind that the total amount of money you end up with must be the same.

Here is what I had in mind. In both cases paper money is used to cover the dollar amount. If only paper money is used then an extra dollar must be used to cover the change. This means that in the all paper money case you will end up with a dollar less in paper money. Since the total amount of money you end up with is the same in both cases, the dollar less in paper money must be compensated for by having a dollar more in change.

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