Associated Topics || Dr. Math Home || Search Dr. Math

How to Turn Word Problems into Algebra Equations

```
Date: 6/6/96 at 7:56:25
From: Anonymous
Subject: Algebra word problems

I am having problems setting up algebra equations from word problems.
I don't know where to put the letters and numbers  Could you please
help?
-Mike
```

```
Date: 6/6/96 at 11:46:18
From: Doctor Anthony
Subject: Re: Algebra word problems

With word problems, you have to express the information in symbolic
form, and that means you use a letter to represent some quantity that
you want to find or need to use in writing down an equation.  For
example you could use 't' to represent time and x to represent
distance.  I will do a couple of examples to illustrate the method,
but of course, every problem will be slightly different, and there is
no ONE way of doing word problems.

(1) A has three times as many sweets as B.  If he gives B six sweets,
he will then have twice as many as B then has.  How many sweets did

Let x = number of sweets that B has initially; then 3x is the number
that A has.  If now A gives 6 sweets to B then A has 3x-6 sweets and B
has x+6 sweets.  Now we are told that after this transfer, A has twice
as many sweets as B, so we can write down an equation to represent
this fact, i.e.

3x-6 = 2(x+6)
3x-6 = 2x + 12
3x-2x = 12 + 6
x = 18

So initially B had 18 sweets and A had 3*18 = 54 sweets.

Check: After transfer B has 18+6 = 24,  A has 54-6 = 48, and 48 is
twice 24.

(2) If a man walks to the station at 3 mph he misses his train by
1 minute. If he runs at 6 mph he has 2 minutes to spare.  Find the
distance to the station.

Let x = distance to the station.  Now we know that the difference in
TIME is 3 minutes between the two methods of travel, so we shall need
to write down an equation involving TIME.

Time = Dist/Speed, so when he walks, time = x/3  (hours)
when he runs, time = x/6  (hours)

Subtract these and equate to the time (in hours) between the two
methods of travel.

x/3 - x/6 = 3/60

x(2-1)/6 = 3/60

x/6 = 3/60

x = 18/60

x = 3/10 of a mile.

So the distance to the station is 3/10 mile.  You can check the result
now by calculating the actual time to walk, and the time to run.

Time to walk = (3/10)/3 = 1/10 hour = 6 minutes
Time to run  = (3/10)/6 = 1/20 hour = 3 minutes
Difference = 3 minutes.

You will note that the important first step is to use letters to
represent unknown quantities so that you can write down equations.
Lay out the work clearly, and express any information given in the
question in terms of the symbols you have introduced.

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

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search