Math Word Problems Demystified - A Self Teaching Guide

2. One number is four times another number.


3. One number is 6 more than twice the other number.


4. One number is 4 less than one-half another number.


5. The difference of two numbers is 12.

SOLUTIONS:

1. Letx¼the first number and 15
   x¼the second number.


2. Letx¼the first number and 4x¼the second number.


3. Letx¼the first number and 2xþ 6 ¼the second number.


4. Letx¼the first number and^12 x
   4 ¼the second number.


5. Letx¼the first number andx
   12 ¼the second number.
   The third skill necessary to solve word problems is to be able to translate
   the given symbols of representation into an equation. Consider these
   examples.

‘‘Three times a number increased by 10 is equal to 28’’ translates to

3 xþ 10 ¼ 28

‘‘Seven times a number decreased by 6 is equal to 29.’’

7 x
 6 ¼ 29

‘‘The difference between a number and one-half itself is equal to 12.’’

x

1

2

x¼ 12

Try These

Translate each into an equation:

1. Seven increased by four times a number is 31.


2. If 5 is subtracted from two times a number, the answer is 15.


3. One half a number plus 8 is equal to 19.


4. Two times a number plus $1.20 is equal to $1.80.


5. The sum of a number and two times itself is equal to 30.

LESSON 8 Algebraic Representation 85