Get numbers from ratios

Question

How to get numbers from ratios? For example:

The number of students in a school is 17500. The ratio between boys and girls is 4:3. How many boys and girls are there?

Not only for this example, but I would like to learn and understand ratio completely. Appreciate if someone guide me on helpful link.

Answer 1

A ratio is a way to show the relative sizes of two (or more) groups. In this case, the ratio is saying that for every group of 4 boys, there are 3 girls. So first we have to find out how much the multiplier for the ratio is, and the following equation does that:

$$4x + 3x = 17500$$ $$7x = 17500$$ $$x = 2500$$

The value $x$ represents what you have to multiply each of the values in the ratio by. Now to solve, we multiply the corresponding number by the multiplier to get the actual amount of students.

Boys = $4 \times 2500 = 10000$

Girls = $3 \times 2500 = 7500$

This is correct since if you add the two amounts together, you get 17,500 students.

Answer 2

You can denote ration by R, now the ratio is also equal to $\frac{x}{y}$ where x is number of boys and y is number of girls so you can say $x=yR$ and you also know $x+y=17500$ substitute the value of x you previously found and work out y and then you can work out x