5 pound book on ratio questions, chapter 20 question 2, and 10.
I have problem with understanding the method of solving such questions. I look at the solutions but the way they assign variable was unfamiliar to me.

for example, in question 2 they assign 2x for boys and then 3x for girls finally they said 2x+3x=5x and the rest is easy, the method wasn’t familiar to me, can you help me understand it?

You can think of ratios as having some kind of “scale”, this “scale” would be applied to both sides of the ratio to generate pairs that match that ratio:

For example, the ratio of Boys:Girls is 2:3

So, we can draw this table:

Scale (x)

Number of Boys

Number of Girls

Total

Total (in terms of Scale x)

1

2 * 1 = 2

3 * 1 = 3

2 + 3 = 5

5 * 1 = 5

2

2 * 2 = 4

3 * 2 = 6

4 + 6 = 10

5 * 2 = 10

3

2 * 3 = 6

3 * 3 = 9

6 + 9 = 15

5 * 3 = 15

x

2 * x = 2x

3 * x = 3x

2x + 3x = 5x

5 * x = 5x

Notice that anything we generate with this will have the ratio of 2 Boys for every 3 Girls.

Also notice that the number of boys is always a multiple of 2, the number of girls is always a multiple of 3, and the total is always a multiple of 5.

When they do 2x+3x=5x , they are essentially deducing that the total number of students must be a multiple of 5.