We see the fractions 5/6 and 3/4. The idea here is to change their denominator to the same first so their units will be the same size/comparable later.

5/6 = 20/24 , 3/4 = 18/24

Let the number of girls be 24 u.
Then, number of boys = 24u + 36


Since 5/6 of girls and 3/4 of boys didn't stay overnight,


1 - 5/6 = 1 - 20/24 = 4/24
So, 1/6 of girls stayed overnight and this equals 4u.


1 - 3/4 = 1/4
Note that 24u + 36 equals 4 groups of (6u + 9).

So 1/4 of boys = 6u + 9
So 1/4 of boys stayed overnight and this equals 6u + 9


Total number of students who stayed overnight
= 4u + 6u + 9
= 10u + 9

So 10u + 9 = 89
10u = 89 - 9 = 80
1u = 80 ÷ 10 = 8

Number of girls who attended the camp

= 24u
= 24 × 8
= 192

Number of boys who attended the camp

= 192 + 36
= 228

Total number of children who attended the camp

= 192 + 228
= 420

Fraction of students who stayed overnight

Number of who stayed overnight / Total

= 89/420


Fraction of students who did not stay overnight

= 1 - 89/420
= 420/420 - 89/420
= 331/420