The ratio of boys to girls in a class is 4:5. If twi girls are absent, the ratio of boys to girls becomes 8:9. How many b are in a class?

To get whole numbers ratio the class must be a mutiple of 9, but we don't know how many (let that be x.)

It will also be a multiple of 17 when two girls are removed (let that be y)

9x - 2 = 17y

As there are two variables you need to create two expressions to make simultaneous equations

trial and error: let x = 4, y must equal 2 as below

36 - 2 = 34

So 16 boys to 20 girls, and 16 boys to 18 girls after absence.

You should derive a second expression for x and y, to solve as simultaneous equations

which you can do because you know the number of boys in each ratio is going to be the same.

If I would use the algebraic method, how would it work?

If you have difficulty with equations, you can apply simple logic:

4:5 could be

4b + 5g

8b + 10g

12b + 15G

16b + 20g

8:9 could be

8b+ 9g

16b + 18g

Note that 18g is 2 less than 20 g.

There are 16 boys.