Solving Word Problems Using Algebra

Solving word problems using algebra consists of the following general steps.

· Identify what is to be found or calculated - the Find variables.

· Identify what is given - the Given statements or equations. For example:

· A value may be given: The length is 8.

· A relationship may be given: The length is twice the width.

· A formula may be implied. The area of a rectangle is 84.

· Assign variable names for each variable. Generally the first letter of the variable name is used. This is the Let statement, and there is a Let statement for each variable.

Consider the following typical word problem:

The sum of 2 numbers is 84. The larger number is 16 more than the smaller. Find the numbers.

· The Find variables are the names of the two numbers. The variable names are the:

· Larger number, resulting in the Let statement: Let L = larger number.

· Smaller, resulting in the Let statement: Let S = smaller number.

· Since the 2 numbers, S and L, are to be found, we have: Find S and Find L

· In the first sentence,

· The sum of 2 numbers translates into S + L.

· is can generally be replaced by the equal sign, =.

· The result is: S + L = 84

· In the second sentence,

· The larger number is translates into L =

· 16 more than the smaller translates into S + 16.

· The result is L = S + 16

· Therefore,

Let S=SMALLER

Let L=LARGER

Find LARGER

Find SMALLER

Given L+S=84

Given L-S=16

The 2 Given equations contain 2 variables, and can be solved resulting in:

L = 50 and S = 34