1Cademy - Solving a Combined-Earnings Word Problem Using Less Than Twice

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Solving a Combined-Earnings Word Problem Using 'Less Than Twice'

Apply the seven-step problem-solving strategy to a real-world word problem in which two people's earnings add up to a known total, and one earning is described using the phrase "less than twice" the other — combining multiplication and subtraction into a single expression.

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?

Read the problem carefully.
Identify what to find: the husband's annual earnings.
Name the unknown: Let $h$ = the amount the husband earns. The phrase " $\$16{,}000$ less than twice what her husband earns" combines two operations: twice signals multiplication by $2$ , and $\$16{,}000$ less than signals subtraction. The wife's earnings are therefore $2h - 16{,}000$ .
Translate into an equation: Together the husband and wife earn $\$110{,}000$ , so: $h + (2h - 16{,}000) = 110{,}000$
Solve the equation. Combine the like terms $h + 2h = 3h$ : $3h - 16{,}000 = 110{,}000$ Add $16{,}000$ to both sides: $3h = 126{,}000$ Divide both sides by $3$ : $h = 42{,}000$ Find the wife's earnings: $2(42{,}000) - 16{,}000 = 84{,}000 - 16{,}000 = 68{,}000$ .
Check: Does $\$42{,}000 + \$68{,}000 = \$110{,}000$ ? $110{,}000 = 110{,}000$ $\checkmark$
Answer: The husband earns $\$42{,}000$ a year.

This example transitions from abstract number problems to a practical financial scenario while using the same algebraic techniques. The phrase "less than twice" produces a subtraction-from-a-multiple expression ( $2h - 16{,}000$ ), and the equation $h + (2h - 16{,}000) = 110{,}000$ requires combining like terms, adding a constant to both sides, and dividing — three steps that mirror the structure seen in earlier number problems. Both unknowns are expressed through a single variable by using the stated relationship between the couple's earnings.

Updated 2026-05-02

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