Difference between revisions of "2021 AMC 10A Problems/Problem 2"
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Revision as of 09:58, 12 February 2021
Contents
[hide]Problem 2
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
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. It follows that Portia's high school has students. We know that or Our answer is
~MRENTHUSIASM
Solution 3 (Quick Inspection)
The number of students in Portia's high school must be a multiple of This eliminates , , and . Since is too small (as is clearly true), we are left with
~MRENTHUSIASM
Video Solution #1(Setting Variables)
https://youtu.be/qNf6SiIpIsk?t=119 ~ThePuzzlr
Video Solution
- pi_is_3.14
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 |
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