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Solving a Two-Step Number Problem Using "Sum" and "Times"
Apply the seven-step problem-solving strategy to a number problem whose translation involves two operations — multiplication by a specific number and addition — producing a two-step equation. Problem: The sum of seven times a number and eight is . Find the number. 1. Read the problem and confirm understanding of all terms. 2. Identify what to find: the number. 3. Name the unknown: Let = the number. 4. Translate by recognizing two keywords: times signals multiplication (here, by ), and sum signals addition. Restate the problem as "The sum of times and is ," which converts to: 5. Solve using two inverse operations. First, subtract from both sides: Then divide both sides by : 6. Check: Is the sum of seven times plus equal to ? 7. Answer: The number is . This problem combining "times" and "sum" generates the equation , which requires both subtraction and division to solve.
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Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
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