2021 AMC 10B Problems/Problem 3: Difference between revisions
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Cross-multiplying and simplifying we get <math>5j=2s.</math> Additionally, since there are <math>28</math> students in the program, <math>j+s = 28.</math> It is now a matter of solving the system of equations <cmath>5j=2s</cmath><cmath>j+s=28,</cmath> and the solution is <math>j = 8, s = 20.</math> Since we want the number of juniors, the answer is <cmath>\boxed{(C) \text{ } 8}.</cmath> | Cross-multiplying and simplifying we get <math>5j=2s.</math> Additionally, since there are <math>28</math> students in the program, <math>j+s = 28.</math> It is now a matter of solving the system of equations <cmath>5j=2s</cmath><cmath>j+s=28,</cmath> and the solution is <math>j = 8, s = 20.</math> Since we want the number of juniors, the answer is <cmath>\boxed{(C) \text{ } 8}.</cmath> | ||
-PureSwag | |||
Revision as of 16:34, 11 February 2021
In an after-school program for juniors and seniors, there is a debate team with an equal number of students from each class on the team. Among the 
students in the program, 
of the juniors and 
of the seniors are on the debate team. How many juniors are in the program?
Solution 1
Say there are 
juniors and 
seniors in the program. Converting percentages to fractions, 
and 
are on the debate team, and since an equal number of juniors and seniors are on the debate team, 
Cross-multiplying and simplifying we get 
Additionally, since there are students in the program, 
It is now a matter of solving the system of equations ![\[5j=2s\]](http://latex.artofproblemsolving.com/e/9/0/e90eca73861ccf271ca585eb49b39608553b1018.png)
![\[j+s=28,\]](http://latex.artofproblemsolving.com/f/2/d/f2d9da87d46e3ec7ee67241f9f6c951877716ebb.png)
and the solution is 
Since we want the number of juniors, the answer is ![\[\boxed{(C) \text{ } 8}.\]](http://latex.artofproblemsolving.com/5/7/2/57218434e7e1414f2a6eff3803ced2168d20ead8.png)
-PureSwag
