2009 Grade 8 CEMC Gauss Problems/Problem 12

Problem

A temperature measured in degrees Celsius ( $C$ ) can be converted to degrees Fahrenheit ( $F$ ) using the formula $F = \frac{9}{5}C + 32$ . If the temperature is $10$ degrees Celsius, what is the temperature in degrees Fahrenheit?

$\text{ (A) }\ -26.4 \qquad\text{ (B) }\ -12.2 \qquad\text{ (C) }\ 75.6 \qquad\text{ (D) }\ 50.0 \qquad\text{ (E) }\ 43.8$

Solution 1

We can simply plug in $10$ for $C$ in the equation given in the original problem:

$F = \frac{9}{5} \times 10 + 32$

$F = 18 + 32$

$F = \boxed {\textbf {(D) } 50.0}$

~anabel.disher

Solution 2 (answer choices)

We can see that $C = \frac{5}{9} \times (F - 32)$ , either from memorization, or by getting $C$ in terms of $F$ .

We can now see that for $C$ to be an integer, $F - 32$ must be an integer divisible by $9$ , due to the fraction having $9$ in the denominator.

This occurs when $F$ is an integer. The only answer choice that can be represented as as an integer is $\boxed {\textbf {(D) } 50.0}$

~anabel.disher

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2009 Grade 8 CEMC Gauss Problems/Problem 12

Problem

Solution 1

Solution 2 (answer choices)