The average cost of a car in 2014 was $28,500, which was $1,500 less than 6 times the average cost in 1975. What was the average cost in 1975?
A$5,000
B$4,750
C$4,500
D$6,000
Answer & Solution
Correct answer: A. $5,000
1. Let c be the average cost of a car in 1975, in dollars.
2. Translate the comparison: 28,500 equals 6c minus 1,500.
3. Add 1,500 to both sides: 6c equals 30,000.
4. Divide both sides by 6: c equals 5,000.
5. Check: 6 times 5,000 dollars is 30,000 dollars, and 1,500 less than that is 28,500, matching the 2014 cost.
6. Dividing 28,500 by 6 straight away gives 4,750, the trap for ignoring the 1,500 dollar adjustment.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 3 "Math Models", section 3.1 Use a Problem-Solving Strategy_
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