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When a teacher counted her students in groups of 4, there were two students left over. When she counted them in groups of 5, she had 1 student left over. If 15 of her students were girls and she had more girls than boys, how many students did she have?

 Feb 21, 2021
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Let n be the number of students. We know that

 

n = 2 (mod 4)

n = 1 (mod 5)

 

15 students are girls, so there is a maximum of 29 students.

 

One solution for n is 26. So, the teacher has 26 students.

 Feb 21, 2021

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