# Interpreting Equations in Word Problems

Instructor: Maria Airth

Maria has a Doctorate of Education and over 20 years of experience teaching psychology and math related courses at the university level.

Word problems are notoriously tricky. They don't need to be! This lesson will help you learn how to analyze word problems to ensure correct solutions are found.

## Interpreting Equations in Word Problems

Oh no, the dreaded word problem! Don't worry; they really aren't as scary as many seem to think. A slow, calm review of a word problem will allow you to discover everything you need to know. Take a deep breath and let's learn how to interpret word problems and check your answers after you are finished.

Sample: You own a chicken coop and decide that you would like to start selling eggs by the dozen. You buy some new egg cartons for \$1.00 a carton and decide to sell the eggs for \$2.50/dozen. Write an equation to determine your profit. Create a chart showing your profit margin if you sell 1 dozen, 3 dozen, 6 dozen, and 10 dozen eggs.

How do you begin to approach this word problem?

The first step is to figure out what you are looking for. Next, you decide how to go about finding it (which operation/equation). Then, you do it (carry out your plan). Finally, look back and check your answer.

Four steps: What, How, Do it, Check it.

Let's work through the sample problem together by using each step.

## Step One

Step one is to figure out what you are looking for. This includes identifying the unknowns in the problem and the desired result or answer.

In our sample problem, we see that one result needs to give us a chart showing the profit margin gained through the sale of multiple sets of eggs. So, profit is an unknown (P).

We need to determine how much profit is made from the sale of a certain number of dozen eggs. That means another unknown (x) is the number of dozen. That will be the variable.

So, x= number of dozen eggs. Our answer should include a chart with dollar amounts in it.

## Step Two

So, how do we work the problem? Let's go back to the words. The operations to use come directly from a few clue words in the word problem. Here are some of the most common words to look for in word problems and their related operations:

• Subtraction: less than, difference, discount, decreased, minus, take away
• Multiply: product, each, twice, per, times
• Divide: quotient, shared, separated into even groups

The first thing to notice in our sample problem is that we must ''spend'' \$1.00 per carton for each dozen eggs. This means we will need to subtract \$1.00 for every dozen eggs. Next, we see that eggs are \$2.50/dozen. This means \$2.50 per dozen. Per is a multiply word. So, we've cracked the code; we'll be multiplying and subtracting in our equation.

Now to write the equation, again based on what we see in the word problem.

The profit will be 2.5x (\$2.50 times the number of dozen) minus 1x (\$1.00 times the number of dozen). This is written algebraically as: 2.5x - x = P; where P is the profit. This will be our equation.

## Step Three

The next step is to solve the word problem using the equation. We know that our result should be in the form of a chart, so we need to plug in the number of dozen (x) into the equation and find the resulting profit (P).

Using this equation, we can fill in a table by substituting each value given for x (1,3,6, and 10).

x 1 3 6 10
y \$1.50 \$4.50 \$9.00 \$15.00

## Step Four

The final step is to analyze the results. Are they logical? Did you make a mathematical error anywhere? Logically, we know that we should arrive at \$5.00 for every two dozen eggs (\$2.50 x 2) and that we need to take off \$2.00 for our costs of the carton on each of those dozen, so we should get \$3.00 for every 2 dozen.

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