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.