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Solving a Two-Number Problem Using "Sum" and "More Than"
Apply the seven-step problem-solving strategy to a number problem involving two unknown numbers that are related by a "more than" phrase and whose sum is given.
Problem: One number is five more than another. The sum of the numbers is . Find the numbers.
- Read the problem.
- Identify what to find: two numbers.
- Name the unknowns using a single variable. Let = the first number. Because one number is "five more than" the other, the second number is .
- Translate into an equation: The sum of the two numbers is , so:
- Solve the equation. First, combine the like terms :
Subtract from both sides:
Divide both sides by :
Find the second number: .
- Check: Is five more than ? . Is their sum ? .
- Answer: The numbers are and .
This example illustrates a key technique for two-unknown number problems: express both quantities through a single variable using the stated relationship ("five more than" becomes ), then write an equation from the remaining fact (the sum). The resulting equation involves combining like terms before using inverse operations to isolate the variable.
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