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### Comparing Numbers: Two Equations, Two Unknowns

```
Date: 01/14/98 at 17:38:46
From: Charles Tollefson
Subject: A problem I'm having trouble with.

Here's the Problem:

One number is 25% of another. The larger number is 12 more than the
smaller. What are the numbers?

What formula can I use to find the answer?
```

```
Date: 01/14/98 at 18:58:14
From: Doctor Barney
Subject: Re: A problem I'm having trouble with.

This is a classic case of two equations and two unknowns.

First let's talk about the unknowns. There are two numbers, but we
don't know what they are, so in order two be able to talk about them,
and write equations for them, we need to make up something to call
them. You can use any names you want, but in algebra it is customary
to use letters, like x and y or a and b or p and q.  How about we use
A and B?

Now we want to write equations using these letters. Read the problem
carefully. The first sentence can be written as a mathematical
equation:

A = (25/100) x B

From the second sentence, we can write another equation, keeping in
mind that from the way we wrote the first equation we know that B is
larger than A.

B = A + 12

Now for the tricky part: if the stuff on the right side of the second
equation is equal to B, we can substitute that stuff in to the first
equation wherever we see a B.  Then the first equation will look like:

A = (25/100) (A+12)

Can you simplify this expression and solve for A?  After you do, take
that value for A and "plug it in" to either of the original two
equations to find the answer for B. The final answer is given below.
(Don't look until you try it yourself.)

-Doctor Barney,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/

```

```
Date: 01/14/98 at 18:47:06
From: Doctor Anthony
Subject: Re: A problem I'm having trouble with.

Let the larger number be x.  Then smaller number is 0.25x

So  x - .25x = 12

.75x = 12

x = 12/.75

= 16

So the two numbers are  16 and  4.

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra

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