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After Batman brought the Joker to justice, the crime rate in Arkham City decreased by $12\%$ . Previously, the crime rate was $c$ incidents per $1000$ people. Which of the following expressions could represent the crime rate in Arkham City after Batman brought the Joker to justice?

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Evaluate two-variable equations: word problems

Full solution

Q. After Batman brought the Joker to justice, the crime rate in Arkham City decreased by

12\%

. Previously, the crime rate was

c

incidents per

1000

people. Which of the following expressions could represent the crime rate in Arkham City after Batman brought the Joker to justice?

Identify Crime Rate: Step $1$ : Identify the original crime rate and the percentage decrease. $\newline$ Original crime rate = $c$ incidents per $1000$ people. $\newline$ Percentage decrease = $12\%$ .
Calculate Decrease: Step $2$ : Calculate the decrease in crime rate. $\newline$ Decrease in crime rate = $12\%$ of $c$ = $0.12 \times c$ .
Determine New Rate: Step $3$ : Determine the new crime rate after the decrease. $\newline$ New crime rate = Original crime rate - Decrease in crime rate = $c - 0.12 \times c = 0.88 \times c$ .

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