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Section 3.5 Applications and Problem Solving 161 Translating Sentences to Mathematical Equations Example 1 A number decreased by 7 is 12. Find the number. Solution: Step 1: Read the problem completely. Let x represent the number. Step 2: Label the unknown. A number decreased by 7 is 12. Step 3: Write the equation in words x Step 4: Translate to a mathematical equation. Step 5: Solve the equation. Add 7 to both sides. 7 12 x 7 12 x 7 7 12 7 x 19 The number is 19. Step 6: Interpret the answer in words. Skill Practice 1. A number minus 6 is 22. Find the number. Avoiding Mistakes To check the answer to Example 1, we see that 19 decreased by 7 is 12. Answers 1. The number is 16. 2. The number is 5. • Example 2 3x 7 11 μ Translating Sentences to Mathematical Equations Seven less than 3 times a number results in 11. Find the number. Solution: Step 1: Read the problem completely. Let x represent the number. Step 2: Label the unknown. Seven less than 3 times Step 3: Write the equation in words. a number results in 11. 7 less than results in 11 Step 4: Translate to a mathematical three times equation. a number Step 5: Solve the equation. Add 7 to both sides. Simplify. Divide both sides by 3. 3x 7 7 11 7 3x 18 3x 3 18 3 x 6 The number is 6. Step 6: Interpret the answer in words. Skill Practice 2. 4 subtracted from 8 times a number is 36. Find the number. Avoiding Mistakes To check the answer to Example 2, we have: The value 3 times 6 is 18, and 7 less than 18 is 11.


miller_prealgebra_2e_ch1_3
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