Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 10"
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Let the number of total students by <math>s</math>, and number of classes by <math>c</math>. Thus, our problem implies that | Let the number of total students by <math>s</math>, and number of classes by <math>c</math>. Thus, our problem implies that | ||
| − | <cmath>\frac{s}{c+1} = 20 \ | + | <cmath>\frac{s}{c+1} = 20 \Longrightarrow s = 20c + 20</cmath> |
| − | <cmath>\frac{s}{c-1} = 30 \ | + | <cmath>\frac{s}{c-1} = 30 \Longrightarrow s = 30c - 30</cmath> |
We solve this system of linear equations to get <math>c = 5</math> and <math>s = 120</math>. Thus, our answer is <math>\frac{s}{c} = \boxed{24}</math>. | We solve this system of linear equations to get <math>c = 5</math> and <math>s = 120</math>. Thus, our answer is <math>\frac{s}{c} = \boxed{24}</math>. | ||
~Bradygho | ~Bradygho | ||
Revision as of 21:30, 10 July 2021
Problem
In a certain school, each class has an equal number of students. If the number of classes was to increase by 
, then each class would have 
students. If the number of classes was to decrease by , then each class would have 
students. How many students are in each class?
Solution
Let the number of total students by 
, and number of classes by 
. Thus, our problem implies that
![\[\frac{s}{c+1} = 20 \Longrightarrow s = 20c + 20\]](http://latex.artofproblemsolving.com/e/6/0/e6049d1834487b9bc02f5f0c68ad29c4df391760.png)
![\[\frac{s}{c-1} = 30 \Longrightarrow s = 30c - 30\]](http://latex.artofproblemsolving.com/c/8/3/c833a5cd563c72c14d2e973828c397ea4aeab4be.png)
We solve this system of linear equations to get 
and 
. Thus, our answer is 
.
~Bradygho
