### Unit 3: Word Problems

Now, let's apply what we learned about solving equations to various types of word problems. To set up the equation, read the word problem carefully to identify the quantity you are being asked to find, the known quantities, and the relationship between them. This is an important skill in algebra since we use algebra to solve many real-world problems.

In this unit, we will identify common types of word problems and discuss how to translate these problems into algebraic equations that can be solved.

**Completing this unit should take you approximately 5 hours.**

Upon successful completion of this unit, you will be able to:

- translate a verbal expression into a variable expression;
- use the basic percent equation to solve problems involving percents;
- apply the basic percent equation to problems involving mixtures, markups, and discounts;
- use the uniform motion equation to solve problems involving uniform motion; and
- create equations in one variable and use them to solve problems.

### 3.1: Mathematical Symbols and Expressions for Common Words and Phrases

Before we can begin solving word problems, we need to understand their language. Common words are used to indicate different types of calculations. For example, when you see the word "difference", it indicates you will be doing subtraction.

Read this page. Pay close attention to the mathematical dictionary table. It may be helpful to copy this table so you can use it as a reference as you become more comfortable working with word problems.

Read through sample sets A and B to see how the word problems are translated into equations. After you read, complete practice sets A and B and check your answers.

### 3.2: Translating Verbal Expression into Mathematical Equations

Now that we know the language, we can begin translating word problems into equations.

Watch these videos which provide step-by-step examples of how to translate word problems into equations we can solve.

### 3.3: Number Problems

The first common type of word problem you will encounter are number problems. These word problems describe numerical operations (addition, subtraction, multiplication, division).

Read the five step method section, which outlines a way to organize your thinking and solve number problems. Note the five steps that set up the equation for a word problem. Then, read the first two examples in sample set A. These examples show how to use the five step method to set up and solve number problems. Finally, do the first two problems in practice set A and check your answers.

### 3.4: Consecutive Integer Problems

The next type of problem we see in algebra are consecutive integer problems. Consecutive integers are integers that follow one another. In other words, we can define the variable

*n*as an integer. Then,*n*+ 1 is the next consecutive integer.Watch these videos. The first shows word problems involving consecutive integers. The second shows a more challenging problem involving the sum of odd integers. When summing odd integers, the equation must be slightly altered.

Read the discussion on consecutive integers, which shows how to write consecutive integers or consecutive even or odd integers. After you read, complete questions 3 and 4 in practice set A and check your answers.

### 3.5: General Statement Problems

Often we can use algebra to solve real-life problems by translating word problems into equations.

Watch this video for examples of these types of problems. Recall the five step method we discussed in section 3.3. When you solve these types of problems, the first key step is to identify the variable.

Read this article for another example of this type of a general statement problem. In this problem, it looks like there are two variables. However, we can relate the quantity of one variable to that of the other. This allows us to write the equation in terms of only one variable.

At the bottom of the page, try a few practice problems and check your answers. Try a couple of these until you feel comfortable writing and solving equations from general word problems.

### 3.6: Applying the Uniform Motion Equation

The uniform motion equation allows us to solve problems involving rate, or speed.

For example, let's say you need to drive 150 miles on the highway with an average speed of 55 miles per hour. How long will it take you to arrive at your destination? We can use a simple formula to solve for the time it will take to drive that distance.

Read the section on the distance, rate, and time formula. We use this equation for all uniform motion problems. Then, do examples 2.58 through 2.60 and check your answers. If you want more practice, you can try exercises 376 and 387.

### 3.7: Value Mixture Problems

Other common types of word problems involve percents, price mark-ups or discounts, and mixtures. In this section we explore these common types of word problems.

Mixture problems involve mixtures of different variables. We can then relate the variables to each other and reduce the problem to one variable.

Watch this video for examples of how to express a mixture problem in an algebraic equation.

Then, watch these videos to see more examples of how to write and solve these types of problems.

After you watch, complete examples 3.26 through 3.32 and check your answers.

Percent problems are also a common type of algebra word problem which often come up when dealing with price mark-ups, sale prices, or calculating tips at restaurants.

Read this section for examples of how to calculate percent from fractions, and how to translate a percent word problems into equations. Pay attention to the formula for finding the percent of change, since we use this formula frequently to determine sale prices.

After you read, complete this assessment and check your answers to practice solving problems with percents.