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/   



ANSWER:  4 and 16

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/