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### Equal Sum, Product, Quotient of Two Numbers

```Date: 10/13/2002 at 20:20:38
From: Liz Ureste
Subject: Math problem

I need to know the sum, product, and quotient of two different numbers
that are all equal. What are the two numbers?

I don't know how to start the problem.
```

```
Date: 10/13/2002 at 22:20:54
From: Doctor Ian
Subject: Re: Math problem

Hi Liz,

Well, if we call the numbers x and y, then we know that the following
must be true:

x + y = x * y

x + y = x / y

x * y = x / y

What we really want to do is get one of these variables (x or y) by
itself on one side of an equation, because then we can substitute for
it in another equation. Let's look at the third equation:

x * y = x / y

x * y * y = x

y * y = x / x

y^2 = 1

y = 1 or -1

That narrows things down considerably. Now let's look at the first
equation. Since y must be 1 or -1, one of the following must be true:

1)  x + 1 = x * 1

2)  x - 1 = x * -1

The first one can't be true for any number, since one operation
changes the value of x and the other doesn't. But what about the
second equation? Can you find a number that makes it true?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra
Middle School Algebra
Middle School Word Problems

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