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Example 3.11 from Elementary Algebra, 3.1 Use a Problem-Solving Strategy
Use a Problem-Solving Strategy: example 3.11
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?
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
Step 1. Read the problem. Step 2. Identify what we are looking for. How much does the husband earn? Step 3. Name. Choose a variable to represent the amount
the husband earns.Let the amount the husband earns. The wife earns $16,000 less than twice that. the amount the wife earns. Step 4. Translate. Together the husband and wife earn $110,000. Restate the problem in one sentence with
all the important information.Translate into an equation. Step 5. Solve the equation. h + 2h − 16,000 = 110,000 Combine like terms. 3h − 16,000 = 110,000 Add 16,000 to both sides and simplify. 3h = 126,000 Divide each side by 3. h = 42,000 $42,000 amount husband earns 2h − 16,000 amount wife earns 2(42,000) − 16,000 84,000 − 16,000 68,000 Step 6. Check. If the wife earns $68,000 and the husband earns $42,000 is the total $110,000? Yes! Step 7. Answer the question. The husband earns $42,000 a year.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
According to the National Automobile Dealers Association, the average cost of a car in 2014 was $28,500. This was $1,500 less than 6 times the cost in 1975. What was the average cost of a car in 1975?
How did it go?