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A married couple together earns $110,000 a year. The wife earns $16,000 less than twice what her husband earns. Which system of equations represents this situation?
Aw+h=110000 and h=2w-16000
Bw-h=110000 and w=2h-16000
Cw+h=110000 and w=2h+16000
Dw+h=110000 and w=2h-16000
Answer & Solution
Correct answer: D. w+h=110000 and w=2h-16000
1. Let h be the amount the husband earns and w be the amount the wife earns.
2. Since the couple earns $110,000 together, the first equation is w plus h equals 110,000.
3. Since the wife earns $16,000 less than twice the husband's amount, the second equation is w equals 2h minus 16,000.
4. Swapping which variable is doubled, using subtraction instead of addition for the total, or adding instead of subtracting the 16,000 would all misrepresent the sentence.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.4 Solve Applications with Systems of Equations_
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