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 "2021 Fall AMC 10B Problems/Problem 4"
Line 2: Line 2:
  
 
<math>(\textbf{A})\: 10\qquad(\textbf{B}) \: 30\qquad(\textbf{C}) \: 60\qquad(\textbf{D}) \: 100\qquad(\textbf{E}) \: 120</math>
 
<math>(\textbf{A})\: 10\qquad(\textbf{B}) \: 30\qquad(\textbf{C}) \: 60\qquad(\textbf{D}) \: 100\qquad(\textbf{E}) \: 120</math>
 +
 +
==Solution==
 +
 +
Let the temperature of Minneapolis at noon be <math>M</math> and let the temperature of St. Louis at noon be <math>S</math>. Then <math>M = N + S</math> and <math>(M-5)-(S+3) = |2| \implies M-S-8 = |2|</math>.
 +
 +
Substituting <math>M</math> into the second equation we have <math>N - 8</math> = |2| \implies N = 10, 6<math>.
 +
 +
The product of all possible values of N is therefore </math>10\cdot6=60=\boxed{C}
 +
 +
~KingRavi

Revision as of 23:48, 22 November 2021

At noon on a certain day, Minneapolis is $N$ degrees warmer than St. Louis. At $4{:}00$ the temperature in Minneapolis has fallen by $5$ degrees while the temperature in St. Louis has risen by $3$ degrees, at which time the temperatures in the two cities differ by $2$ degrees. What is the product of all possible values of $N?$

$(\textbf{A})\: 10\qquad(\textbf{B}) \: 30\qquad(\textbf{C}) \: 60\qquad(\textbf{D}) \: 100\qquad(\textbf{E}) \: 120$

Solution

Let the temperature of Minneapolis at noon be $M$ and let the temperature of St. Louis at noon be $S$. Then $M = N + S$ and $(M-5)-(S+3) = |2| \implies M-S-8 = |2|$.

Substituting $M$ into the second equation we have $N - 8$ = |2| \implies N = 10, 6$.

The product of all possible values of N is therefore$ (Error compiling LaTeX. Unknown error_msg)10\cdot6=60=\boxed{C}

~KingRavi

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2021_Fall_AMC_10B_Problems/Problem_4&oldid=165272"