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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 was $28{,}400. This was $1{,}600 less than six times the cost in . What was the average cost of a car in ?
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Read the problem carefully. The goal is to find a past cost using a present cost.
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Identify what to find: the average cost of a car in .
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Name the unknown: Let = the average cost of a car in . The phrase "$1{,}600 less than six times the cost in " tells us that the cost in can be expressed as .
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Translate into an equation: The average cost in was $28{,}400, so:
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Solve the equation. Combine the two operations by first adding 1{,}600 to both sides: Divide both sides by :
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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
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Answer: The average cost of a car in 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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OpenStax
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.
As a financial historian, you are investigating vehicle pricing trends over the last few decades. You are analyzing the following statement: 'The average cost of a car in 2014 was ${}28{,}400, which was ${}1{,}600 less than six times the average cost in 1975.' To determine the exact cost in 1975, you must translate this narrative into an algebraic equation. Match each mathematical component to its specific role or meaning within this problem.
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As a budget analyst reviewing historical equipment expenses, you must translate verbal financial descriptions into algebraic expressions. True or False: The comparative phrase '$1{,}200 less than four times the historical cost ' is correctly represented by the algebraic expression .
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