# 2023 AMC 8 Problems/Problem 3

## Problem

Wind chill is a measure of how cold people feel when exposed to wind outside. A good estimate for wind chill can be found using this calculation $$(\text{wind chill}) = (\text{air temperature}) - 0.7 \times (\text{wind speed}),$$ where temperature is measured in degrees Fahrenheit $(^{\circ}\text{F})$ and the wind speed is measured in miles per hour (mph). Suppose the air temperature is $36^{\circ}\text{F}$ and the wind speed is $18$ mph. Which of the following is closest to the approximate wind chill?

$\textbf{(A)}\ 18 \qquad \textbf{(B)}\ 23 \qquad \textbf{(C)}\ 28 \qquad \textbf{(D)}\ 32 \qquad \textbf{(E)}\ 35$

## Solution

By substitution, we have \begin{align*} (\text{wind chill}) &= 36 - 0.7 \times 18 \\ &= 36 - 12.6 \\ &= 23.4 \\ &\approx \boxed{\textbf{(B)}\ 23}. \end{align*} ~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, MRENTHUSIASM

## Solution 2: Estimation

$0.7$ is very close to $\frac{2}{3}$ - therefore, we can substitute $\frac{2}{3}$ into the equation to get $36 - \frac{2}{3} * 18$, which is $36 - 12 = 24$. As $\frac{2}{3}$ is slightly less than $0.7$, the correct answer is slightly less than $24$. Therefore, the answer is $\boxed{\textbf{(B)}\ 23}$.

~TheGoldenRetriever

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