Question

6) When a teacher counted her students in groups of 4, there were 2 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??
This needs to be shown full work for full credit on my college math class I need help it’s due this Wednesday!!!

Answer 1

Answer:

The solution is that there are 26 students in her class

Step-by-step explanation:

We know that 15 of her student are girls, and since there are more girls than boys in the class, there can at most be 15+14= 29 students in her class.

We need to find a number x between 16 (in the case where there is only one boy in the class) and 29, for which x/4 gives a remainder of 2, and x/5 gives a remainder of 1.

The numbers between 16 and 29, which when divided by 4 gives a remainder of 2 are:

18, 22, and 26

You can check yourself that these give a remainder of 2.

So it is one of these numbers. But the solution must also fulfill that the number divided by 5 gives a remainder of 1.

18/5 = 15 + remainder=3

22/5 = 4 + remainder=2

26/5 = 5 + remainder=1

Thus the only possible solution is 26.