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Solving a Two-Step Number Problem Using "Sum" and "Twice"
Apply the seven-step problem-solving strategy to a number problem whose translation involves two operations — multiplication and addition — producing a two-step equation.
Problem: The sum of twice a number and seven is . Find the number.
- Read the problem and confirm understanding of all terms.
- Identify what to find: the number.
- Name the unknown: Let = the number.
- Translate by recognizing two keywords: twice signals multiplication by , and sum signals addition. Restate the problem as "The sum of twice and is ," which converts to:
- Solve using two inverse operations. First, subtract from both sides:
Then divide both sides by :
- Check: Is the sum of twice and equal to ?
- Answer: The number is .
Unlike one-step number problems where a single keyword produces a single-operation equation, this problem combines two keywords ("twice" and "sum") to generate , which requires both subtraction and division to solve. As comfort grows, intermediate steps may be condensed — but writing out every step is perfectly fine while building confidence.
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