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Solving a Word Problem for the Number of Boys in a Study Group
Apply the seven-step problem-solving strategy to a word problem in which one quantity is described using two combined operations — multiplication and addition — applied to the unknown.
Problem: In a study group, the number of girls was three more than twice the number of boys. There were girls. How many boys were in the study group?
- Read the problem carefully and confirm that every word is understood.
- Identify what to find: the number of boys in the study group.
- Name the unknown: Let = the number of boys.
- Translate into an equation: The phrase "three more than twice the number of boys" combines two operations — "twice" signals multiplication by , and "three more than" signals adding to that product. So the number of girls equals . Since there are girls:
- Solve using a two-step process. First, subtract from both sides to undo the addition:
Then divide both sides by to isolate :
- Check: Is boys reasonable for a study group? Yes. Does "three more than twice " equal ? Twice is ; three more than is .
- Answer: There were boys in the study group.
This example shows how the phrase "more than twice" combines multiplication and addition into a single algebraic expression, producing a two-step equation that requires both subtraction and division to solve. Unlike problems where the translation involves only one operation, multi-operation phrases demand careful attention to the order in which the operations are applied to the unknown.
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