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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 3636. 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 nn = the number. 4. Translate by recognizing two keywords: times signals multiplication (here, by 77), and sum signals addition. Restate the problem as "The sum of 77 times nn and 88 is 3636," which converts to: 7n+8=367n + 8 = 36 5. Solve using two inverse operations. First, subtract 88 from both sides: 7n+88=3687n + 8 - 8 = 36 - 8 7n=287n = 28 Then divide both sides by 77: 7n7=287\frac{7n}{7} = \frac{28}{7} n=4n = 4 6. Check: Is the sum of seven times 44 plus 88 equal to 3636? 74+8=?367 \cdot 4 + 8 \stackrel{?}{=} 36 28+8=?3628 + 8 \stackrel{?}{=} 36 36=3636 = 36 \checkmark 7. Answer: The number is 44. This problem combining "times" and "sum" generates the equation 7n+8=367n + 8 = 36, which requires both subtraction and division to solve.

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Updated 2026-05-02

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