Difference between revisions of "2021 AMC 10A Problems/Problem 2"
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~MRENTHUSIASM | ~MRENTHUSIASM | ||
− | ==Video Solution 1 (Very Fast & Simple)== | + | ==Video Solutions== |
+ | ===Video Solution 1 (Very Fast & Simple)=== | ||
https://youtu.be/DOtysU-a1B4 | https://youtu.be/DOtysU-a1B4 | ||
~ Education, the Study of Everything | ~ Education, the Study of Everything | ||
− | ==Video Solution 2 (Setting Variables) == | + | ===Video Solution 2 (Setting Variables)=== |
https://youtu.be/qNf6SiIpIsk?t=119 | https://youtu.be/qNf6SiIpIsk?t=119 | ||
~ThePuzzlr | ~ThePuzzlr | ||
− | ==Video Solution 3 (Solving by Equation) == | + | ===Video Solution 3 (Solving by Equation)=== |
https://www.youtube.com/watch?v=aOpgeMfvUpE&list=PLexHyfQ8DMuKqltG3cHT7Di4jhVl6L4YJ&index=1 | https://www.youtube.com/watch?v=aOpgeMfvUpE&list=PLexHyfQ8DMuKqltG3cHT7Di4jhVl6L4YJ&index=1 | ||
~North America Math Contest Go Go Go | ~North America Math Contest Go Go Go | ||
− | ==Video Solution 4== | + | ===Video Solution 4=== |
https://youtu.be/xXx0iP1tn8k | https://youtu.be/xXx0iP1tn8k | ||
- pi_is_3.14 | - pi_is_3.14 | ||
− | ==Video Solution 5== | + | ===Video Solution 5=== |
https://youtu.be/GwwDQYqptlQ | https://youtu.be/GwwDQYqptlQ | ||
~savannahsolver | ~savannahsolver | ||
− | ==Video Solution 6== | + | ===Video Solution 6=== |
https://youtu.be/50CThrk3RcM?t=66 | https://youtu.be/50CThrk3RcM?t=66 | ||
~IceMatrix | ~IceMatrix | ||
− | ==Video Solution 7 (Problems 1-3)== | + | ===Video Solution 7 (Problems 1-3)=== |
https://youtu.be/CupJpUzKPB0 | https://youtu.be/CupJpUzKPB0 | ||
~MathWithPi | ~MathWithPi | ||
− | ==Video Solution 8== | + | ===Video Solution 8=== |
https://youtu.be/slVBYmcDMOI | https://youtu.be/slVBYmcDMOI | ||
Revision as of 07:46, 18 August 2021
Contents
Problem
Portia's high school has times as many students as Lara's high school. The two high schools have a total of students. How many students does Portia's high school have?
Solution 1 (Two Variables)
The following system of equations can be formed with representing the number of students in Portia's high school and representing the number of students in Lara's high school. Substituting with we get . Solving for , we get . Since we need to find we multiply by 3 to get , which is
-happykeeper
Solution 2 (One Variable)
Suppose Lara's high school has students, so Portia's high school has students. We have or The answer is
~MRENTHUSIASM
Solution 3 (Arithmetic)
Clearly, is times the number of students in Lara's high school. Therefore, Lara's high school has students, and Portia's high school has students.
~MRENTHUSIASM
Solution 4 (Answer Choices)
Solution 4.1 (Quick Inspection)
The number of students in Portia's high school must be a multiple of This eliminates and Since is too small (as it is clear that ), we are left with
~MRENTHUSIASM
Solution 4.2 (Plug in the Answer Choices)
For we have So, is incorrect.
For we have So, is incorrect.
For we have So, is correct.
For completeness, we will check answer choices and
For we have So, is incorrect.
For we have So, is incorrect.
~MRENTHUSIASM
Video Solutions
Video Solution 1 (Very Fast & Simple)
~ Education, the Study of Everything
Video Solution 2 (Setting Variables)
https://youtu.be/qNf6SiIpIsk?t=119 ~ThePuzzlr
Video Solution 3 (Solving by Equation)
https://www.youtube.com/watch?v=aOpgeMfvUpE&list=PLexHyfQ8DMuKqltG3cHT7Di4jhVl6L4YJ&index=1 ~North America Math Contest Go Go Go
Video Solution 4
- pi_is_3.14
Video Solution 5
~savannahsolver
Video Solution 6
https://youtu.be/50CThrk3RcM?t=66
~IceMatrix
Video Solution 7 (Problems 1-3)
~MathWithPi
Video Solution 8
~The Learning Royal
See Also
2021 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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.