2023 AMC 8

Complete problem set with solutions and individual problem pages

Problem 3 Easy

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?

  • A.

    18

  • B.

    23

  • C.

    28

  • D.

    32

  • E.

    35

Answer:B

Solution 1

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*}

 

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} \cdot 18 = 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}.

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