Translating Problems into Equations

August 23, 2011

Translating Problems into Equations

Objective To translate simple word problems into equations.

Word Problems

A word problem describes a situation in which certain numbers are related toeach other. Some of these numbers are given in the problem and are consideredto be known numbers. Other numbers are at first unknown. You must determinetheir values by using the facts of the problem.

Word Problems

Simple word problems often give two facts involving two unknowns. Thefollowing steps can be used to translate such problems into equations. (In alater section, you will learn to find the solution of the problem by solving theequation.)

Word Problems

Step 1 Read the problem carefully.

• Decide what the unknowns are.

• Decide what the facts are.

Word Problems

Step 2 Choose a variable and represent the unknowns.

• Write an expression for the other unknown using the variableand one of the facts.

• Choose a variable for one unknown.

Word Problems

Step 3 Reread the problem and write an equation.

• Use the other fact from the problem to write an equation.

Example 1

Translate this problem into an equation.

1. Marta has twice as much money as Heidi.

2. Together they have $36.

How much money does each have?

Example 1

Solution Use the three steps shown above.

Step 1 The unknowns are the amounts of money Marta and Heidi have. Each of thenumbered sentences gives you a fact.

Example 1

Step 2

Let h = Heidi's amount.

Use h and sentence (1):

Then 2h = Marta's amount.

Choose a variable:

Example 1

Step 3

ℎ + 2ℎ = 36

Use sentence (2) to write an equation:

Problems Involving Lengths

If a word problem involves lengths or distances, a sketch can help you toanalyze the problem. Example 2 illustrates this.

Example 2

Translate this problem into an equation.

1. A wooden rod 60 in. long is sawed into two pieces.

2. One piece is 4 in. longer than the other.

What are the lengths of the pieces ?

Example 2

Solution Use the three steps shown above.

Step 1 The unknowns are the lengths of the pieces.Sentences (1) and (2) each give a fact.

Example 2

Step 2

Let x = the shorter length.

Use x and sentence (2):

Then x + 4 = the longer length.

Choose a variable:

x x 4

Example 2

Step 3

𝑥 + 𝑥 + 4 = 60

Use sentence (1) to write an equation:

Homework

p 24: problems 1-12, p 25: problems 13-19 odd,

p 26: Mixed Review