At the end of the year, cars made in the current year are marked down to make room for next year's models. One particular model has a sale price of $\$41,705$ , which is $5\%$ less than it sold for when it was new. What was the original price of the vehicle? $\newline$ $\$$ ____

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Grade 8

Percent of change: find the original amount word problems

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Q. At the end of the year, cars made in the current year are marked down to make room for next year's models. One particular model has a sale price of

\$41,705

, which is

5\%

less than it sold for when it was new. What was the original price of the vehicle?

\newline

\$

____

Set $x$ as original price: Step $1$ : Let $x$ be the original price of the car. $\newline$ Reasoning: The sale price is $5\%$ less than the original price. $\newline$ Calculation: Sale price = $x - 0.05x = 0.95x$ $\newline$ Math error check:
Equation with sale price: Step $2$ : Set up the equation using the given sale price. $\newline$ Reasoning: We know the sale price is $\$41,705$ . $\newline$ Calculation: $0.95x = 41,705$ $\newline$ Math error check:
Solve for original price: Step $3$ : Solve for $x$ , the original price. $\newline$ Reasoning: Divide both sides of the equation by $0.95$ to isolate $x$ . $\newline$ Calculation: $x = \frac{41,705}{0.95}$ $\newline$ Math error check: