Difference between revisions of "2021 AMC 10A Problems/Problem 2"
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− | ==Solution 3 (Quick Inspection)== | + | ==Solution 3 (Arithmetics)== |
+ | Clearly, <math>2600</math> students is <math>4</math> times as many students as Lara's high school. Therefore, Lara's high school has <math>2600\div4=650</math> students, and Portia's high school has <math>650\cdot3=\boxed{\textbf{(C)} ~1950}</math> students. | ||
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+ | ~MRENTHUSIASM | ||
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+ | ==Solution 4 (Quick Inspection)== | ||
The number of students in Portia's high school must be a multiple of <math>3.</math> This eliminates <math>\textbf{(B)}</math>, <math>\textbf{(D)}</math>, and <math>\textbf{(E)}</math>. Since <math>\textbf{(A)}</math> is too small (as <math>600+600/3<2600</math> is clearly true), we are left with <math>\boxed{\textbf{(C)} ~1950}.</math> | The number of students in Portia's high school must be a multiple of <math>3.</math> This eliminates <math>\textbf{(B)}</math>, <math>\textbf{(D)}</math>, and <math>\textbf{(E)}</math>. Since <math>\textbf{(A)}</math> is too small (as <math>600+600/3<2600</math> is clearly true), we are left with <math>\boxed{\textbf{(C)} ~1950}.</math> | ||
Revision as of 03:24, 14 February 2021
Contents
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 (Arithmetics)
Clearly, students is times as many students as Lara's high school. Therefore, Lara's high school has students, and Portia's high school has students.
~MRENTHUSIASM
Solution 4 (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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.