2021 AMC 10A Problems/Problem 2
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 gives Solving for gives Since we need to find we multiply by to get
~happykeeper (Solution)
~MRENTHUSIASM (Reformatting)
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 (Observations)
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
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.