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 | |
| + | <cmath>\frac{s}{c+1} = 20 \rightarrow s = 20c + 20</cmath> | ||
| + | <cmath>\frac{s}{c-1} = 30 \rightarrow 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>. | ||
| + | |||
| + | ~Bradygho | ||
Revision as of 21:29, 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
![\[\frac{s}{c+1} = 20 \rightarrow s = 20c + 20\]](http://latex.artofproblemsolving.com/0/1/2/012ce853aa2884cbe92553119e61dcb982eaf620.png)
![\[\frac{s}{c-1} = 30 \rightarrow s = 30c - 30\]](http://latex.artofproblemsolving.com/2/7/8/27824ed31337cef387b9c51332a641c81d5f5b5a.png)
We solve this system of linear equations to get 
and 
. Thus, our answer is 
.
~Bradygho
