Translating a Combined-Earnings Word Problem into a System of Equations
Apply the first four steps of the problem-solving strategy for systems of linear equations to translate a real-world earnings problem into a system without solving it.
Problem: A married couple together earns $110,000 a year. The wife earns $16,000 less than twice what her husband earns. What does the husband earn?
- Identify what to find: the amount that the husband and wife each earn.
- Name the unknowns: Let = the amount the husband earns and = the amount the wife earns.
- Translate each verbal relationship into an equation:
- "A married couple together earns $110,000" translates to .
- "The wife earns $16,000 less than twice what her husband earns" translates to .
- The resulting system is:
Compare this with the single-variable approach to the same problem, where the wife's earnings must be expressed as and then substituted into a single equation . The systems approach lets each person's earnings keep its own variable, making the initial setup more direct — each fact in the problem becomes its own equation.
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Ch.5 Systems of Linear Equations - Elementary Algebra @ OpenStax
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