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Solving a Word Problem for the Past Cost of a Car
Apply the seven-step problem-solving strategy to a real-world word problem that asks to find an unknown past value based on a known present value and a related comparative phrase.
Problem: According to the National Automobile Dealers Association, the average cost of a car in 2014 was $28,400. This was $1,600 less than six times the cost in 1975. What was the average cost of a car in 1975?
- Read the problem carefully. The goal is to find a past cost using a present cost.
- Identify what to find: the average cost of a car in 1975.
- Name the unknown: Let = the average cost of a car in 1975. The phrase "$1,600 less than six times the cost in 1975" tells us that the cost in 2014 can be expressed as .
- Translate into an equation: The average cost in 2014 was $28,400, so:
- Solve the equation. Combine the two operations by first adding 1,600 to both sides: Divide both sides by 6:
- Check: Is $1,600 less than six times $5,000 equal to $28,400? 6(5{,}000) - 1{,}600 stackrel{?}{=} 28{,}400 30{,}000 - 1{,}600 stackrel{?}{=} 28{,}400 28{,}400 = 28{,}400 checkmark
- Answer: The average cost of a car in 1975 was $5,000.
This problem highlights translating comparative language into an equation. The expression accurately captures the relationship, which directly translates into a two-step equation.
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Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
Algebra
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Learn After
As a logistics coordinator, you are reviewing historical equipment costs. The current average cost of a delivery van is {}42{,}500. Your company's financial records note that this current cost is {}2{,}500 less than five times the cost of a similar van back in the year 2000.
If represents the average cost of a van in the year 2000, which of the following equations correctly represents this relationship?
You are a junior accountant at a logistics firm tasked with verifying historical asset costs for a tax audit. To find the average cost of a car in 1975, given that its 2014 cost of $28{,}400 was $1{,}600 less than six times the original cost, you must apply the standard seven-step problem-solving strategy. Arrange the following core steps of that strategy in the correct sequence.
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