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.
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.
3.2: Translating Verbal Expression into Mathematical Equations
Now that we know the language, we can begin translating word problems into equations.
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).
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.
3.5: General Statement Problems
Often we can use algebra to solve real-life problems by translating word problems into equations.
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.
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.