Based on key information in the word problem, you know that it cost $50.25 to set up the lemonade stand. You also know that a cup of lemonade costs $.075. These are the numbers that will appear in your equation.
Let's Break it Down
You may recall that an algebraic expression contains a number, a variable—or a combination of numbers and variables—and at least one arithmetic operation such as addition, subtraction, multiplication, or division. An algebraic equation, on the other hand, makes a statement. It states that two expressions are equal, using an equal sign “ = ”.
Before you can use algebra to solve some of the problems you encounter in daily life (at school, at home, or on the job), you need to be able to translate a verbal representation—the words used to describe a problem into a mathematical expression or equation—one that correctly indicates the mathematical operations involved. The most common operations, of course, are adding, subtracting, multiplying and dividing (+, −, ×, ÷).
It’s important to remember that there is more than one way to describe each of the basic operations. Study the table below to review some of the words and phrases that are used to express math equations as verbal representations. When you see or hear these words used to describe a problem, you’ll need to know which operation to include in your equation. (Note that these are just a few examples—you may encounter others from time to time.)
| Addition | plus, added to, increased by, more than, together |
| Subtraction | decreased by, less than, less, minus, subtracted from, difference, fewer than |
| Multiplication | times, multiplied by, product of |
| Division | divided by, ratio, quotient, per, out of, percent (of 100) |
| Equals | totals, yields, is, equals, gives, will be, was, are |
Example
Let’s try translating a word problem into an algebraic equation—so that we can more easily solve it. Read through the problem scenario below.
The cost of setting up a lemonade stand is $50.25. You can sell each cup of lemonade for $0.75. For you to break even, the product of the price of each cup and the number of cups sold must equal the total cost of setting up the lemonade stand.
The slideshow below demonstrates how to translate the verbal representation above into an algebraic equation that correctly represents the situation.
Give it a shot!
Read through the problem scenario below
Laurie spent $27 on shoes, which was $11 less than twice what she spent on a pair of jeans.
Answer each question, then click the question to check your work.
Key information: The cost of shoes is $27. |
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\(\mathsf{ $27 = 2J - $11 }\) |
