Solving an Age Word Problem Using a System of Equations by Substitution
Apply the seven-step problem-solving strategy for systems of linear equations to a real-world age problem, using substitution to solve the resulting system.
Problem: Devon is 26 years older than his son Cooper. The sum of their ages is 50. Find their ages.
- Read the problem.
- Identify what to find: the ages of Devon and Cooper.
- Name the unknowns: Let = Devon's age and = Cooper's age.
- Translate into a system of equations. "Devon is 26 years older than Cooper" gives . "The sum of their ages is 50" gives . The system is:
- Solve using substitution. Because the first equation is already solved for , substitute for in the second equation:
Combine like terms: . Subtract 26 from both sides: . Divide both sides by 2: .
Substitute into the first equation:
- Check: Is Devon's age 26 more than Cooper's? ✓. Is the sum of their ages 50? ✓.
- Answer: Devon is 38 and Cooper is 12 years old.
This example applies the systems approach to an age problem — a common real-world context where one person's age is described relative to another's. The phrase "is 26 years older than" translates directly into an equation already solved for one variable (), making substitution a natural choice. The structure mirrors abstract number problems — one equation for a sum and one for a relationship between the unknowns — but uses a concrete, relatable scenario involving ages.
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