Difference between revisions of "2021 Fall AMC 10B Problems/Problem 4"
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<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== | + | ==Solution 1== |
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>. | 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>. | ||
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~KingRavi | ~KingRavi | ||
+ | |||
+ | == Solution 2 == | ||
+ | <cmath> | ||
+ | \begin{align*} | ||
+ | | N - 5 - 3 | = 2 . | ||
+ | \end{align*} | ||
+ | </cmath> | ||
+ | |||
+ | Hence, <math>N = 10</math> or 6. | ||
+ | |||
+ | Therefore, the answer is <math>\boxed{\textbf{(C) }60}</math>. | ||
+ | |||
+ | ~Steven Chen (www.professorchenedu.com) | ||
+ | |||
==Video Solution by Interstigation== | ==Video Solution by Interstigation== | ||
https://youtu.be/p9_RH4s-kBA?t=291 | https://youtu.be/p9_RH4s-kBA?t=291 |
Revision as of 22:17, 25 November 2021
Problem
At noon on a certain day, Minneapolis is degrees warmer than St. Louis. At
the temperature in Minneapolis has fallen by
degrees while the temperature in St. Louis has risen by
degrees, at which time the temperatures in the two cities differ by
degrees. What is the product of all possible values of
Solution 1
Let the temperature of Minneapolis at noon be and let the temperature of St. Louis at noon be
. Then
and
.
Substituting into the second equation we have
.
The product of all possible values of N is therefore
~KingRavi
Solution 2
Hence, or 6.
Therefore, the answer is .
~Steven Chen (www.professorchenedu.com)
Video Solution by Interstigation
https://youtu.be/p9_RH4s-kBA?t=291
See Also
2021 Fall AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.