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### Two Coins Problem

```Date: 11/22/2006 at 11:23:24
From: Anne
Subject: Two US coins total fifty-five cents, but one is not a nickel

I have two U.S. coins that when added together total fifty-five cents,
but one is not a nickel.  What two coins do I have?

I cannot come up with a combination of two coins that would equal
fifty-five cents without using a nickel.  This is a problem that was
given to my 8 year old son.

Possibilities:

a fifty-cent coin + a nickel = .55, but uses a nickel
a one dollar coin - a fifty cent coin = .50
a one dollar coin - a quarter = .75
two quarters = .50
one quarter plus one dime = .35

What am I missing?

```

```
Date: 11/22/2006 at 11:49:50
From: Doctor Douglas
Subject: Re: Two US coins total fifty-five cents, but one is not a nickel

Hi, Anne.

This is a classic "language" or "logic" problem that is usually
presented to practice "critical thinking".  Many people do not like
the answer, because it seems more like a trick.

A "fifty-cent coin + a nickel" indeed adds up to fifty-five cents.
One of the coins (the nickel), is a nickel, and the other coin (the
half-dollar) is obviously *not* a nickel.  So this solution contains a
coin that "is not a nickel", and thus satisfies the requirements.

You already found the correct answer, but the phrasing of the problem
led you to reject it.  That's the point of this problem--to make you
examine precisely what the words say.

One thing to consider is exactly how you could rephrase the question
so that this confusion is avoided, and thereby rendering the problem
trivial instead of puzzling.  Adding two small words goes a long way:
"Two US coins added together total fifty-five cents, but one [of
them] is not a nickel.  What are the two coins?".

- Doctor Douglas, The Math Forum
http://mathforum.org/dr.math/

```

```
Date: 11/22/2006 at 12:32:35
From: Anne
Subject: Thank you (Two US coins total fifty-five cents, but one is
not a nickel)

Thank you for clearing this up!  The answer was right in front of me,
but I was focused on the wording and it confused me.  Thank you so much!
```
Associated Topics:
Elementary Word Problems
Middle School Word Problems

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