finding the total number of students given two ratios

Question

The ratio of boys to girls in a class is 3:4 in a certain day when 3 boys are absent the ratio becomes 5:8 what is the total number of students

Answer 1

3x:4x when all are present

(3x-3):4x when 3 boys are absent

this equals 5x:8x

(3x-3)/4x=5x/8x

cross multiply

20x^2=24x^2-24x

24x^2-20x^2-24x=0

4x^2-24x=0

x^2-6x=0

x(x-6)=0

x-6=0

x=6

6*3=18 and 6*4=24 for a total of 18+24=42 students

18/24=3/4

(18-3)/24=15/24=5/8

or,...

3 to 4  or 0 to 4

6 to 8 or 3 to 8

9 to 12 or 6 to 12

12 to 16 or 9 to 16

15 to 20 or 12 to 20

18 to 24 or 15 to 24 which equals 5 to 8 so there are 18+24=42 students