160 Chapter 3 Solving equations Problem-Solving Flowchart for Word Problems Step 1 Read the • Familiarize yourself with the problem. problem Estimate the answer if possible. completely. Step 2 Assign • Identify the unknown quantity or quantities. Let labels to a variable represent one of the unknowns. Draw unknown a picture and write down relevant formulas when quantities. appropriate. Step 3 Write an • Verbalize what quantities must be equal. equation in words. Step 4 Write a • Replace the verbal equation with a mathematical mathematical equation using x or some other variable. equation. Step 5 Solve the • Solve for the variable using the steps for solving equation. linear equations. Step 6 Interpret the • Once you have obtained a numerical value for results and the variable, recall what it represents in the write the final context of the problem. Can this value be used answer in to determine other unknowns in the problem? words. Write an answer to the word problem in words. 2. Translating Verbal Statements into Equations We begin solving word problems with practice translating between an English sentence and an algebraic equation. First, spend a minute to recall some of the key words that represent addition, subtraction, multiplication, and division. See Table 3-4. Addition: a b Subtraction: a b The sum of a and b The difference of a and b a plus b aminus b b added to a bsubtracted from a b more than a adecreased by b a increased by b bless than a The total of a and b Multiplication: Division: a b The product of a and b The quotient of a and b a times b adivided by b a multiplied by b bdivided into a The ratio of a and b a over b a per b a b Table 3-4 Avoiding Mistakes It is always a good idea to check your answer in the context of the problem. This will help you determine if your answer is reasonable.
miller_prealgebra_2e_ch1_3
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