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A town's employment statistics show that $867$ of its residents were unemployed last month. This is a decrease of $15\%$ from the previous month. How many residents were unemployed in the previous month? The algebraic equation is $\square=867$ . (Type an expression using $x$ as the variable. Use integers or decimals for any numbers in the expression. Do not simplify.) A total of residents were unemployed in the previous month. (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.)

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Interpret parts of quadratic expressions: word problems

Full solution

Q. A town's employment statistics show that

867

of its residents were unemployed last month. This is a decrease of

15\%

from the previous month. How many residents were unemployed in the previous month? The algebraic equation is

\square=867

. (Type an expression using

x

as the variable. Use integers or decimals for any numbers in the expression. Do not simplify.) A total of residents were unemployed in the previous month. (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.)

Define variable $x$ : question_prompt: Calculate the number of residents who were unemployed in the previous month based on a $15\%$ decrease to $867$ residents last month.
Simplify equation: Step $1$ : Define the variable $x$ to represent the number of unemployed residents in the previous month. Since the number decreased by $15\%$ , the equation is $x - 0.15x = 867$ .
Solve for x: Step $2$ : Simplify the equation. Combine like terms on the left side: $\newline$ $x - 0.15x = 0.85x$ $\newline$ So, $0.85x = 867$ .
Solve for x: Step $2$ : Simplify the equation. Combine like terms on the left side: $\newline$ $x - 0.15x = 0.85x$ $\newline$ So, $0.85x = 867$ . Step $3$ : Solve for x by dividing both sides of the equation by $0.85$ : $\newline$ $x = \frac{867}{0.85}$ $\newline$ $x \approx 1020.0$

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