Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2009 Grade 8 CEMC Gauss Problems/Problem 12"

(Created page with "==Problem== A temperature measured in degrees Celsius (<math>C</math>) can be converted to degrees Fahrenheit (<math>F</math>) using the formula <math>F = \frac{9}{5}C + 32</m...")
 
 
Line 1: Line 1:
 
==Problem==
 
==Problem==
 +
{{delete|page was moved}}
 
A temperature measured in degrees Celsius (<math>C</math>) can be converted to degrees Fahrenheit (<math>F</math>) using the formula <math>F = \frac{9}{5}C + 32</math>. If the temperature is <math>10</math> degrees Celsius, what is the temperature in degrees Fahrenheit?
 
A temperature measured in degrees Celsius (<math>C</math>) can be converted to degrees Fahrenheit (<math>F</math>) using the formula <math>F = \frac{9}{5}C + 32</math>. If the temperature is <math>10</math> degrees Celsius, what is the temperature in degrees Fahrenheit?
  

Latest revision as of 12:08, 1 October 2025

Problem

This page has been proposed for deletion. Reason: page was moved

Note to sysops: Before deleting, please review: • What links here • Discussion page • Edit history

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2009_Grade_8_CEMC_Gauss_Problems/Problem_12&oldid=262018"