Question

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?

Answer 1

There’s 16 students - 15 girls and 1 boy

Number of students in class = x students

X is two more than a multiple of 4

So x is an even number because multiples of 4 are even & adding 2 would mean it’s still equal

X is 1 more than a multiple of 5. We know x is an even number. It has to be a multiple of 5 ending in 5 not 0
5 + 1 = 6

All multiples of 4 ending in 6 are 16, 36, 56...

Since there are 15 girls and there are less boys than girls

16 - 15 = 1

Therefore there’s 16 students