Question

The ratio of boys to girls in a class is \[2:4\]. If there are 24 students total in the class, how many of them are boys?

Answer 1

Hint: We use the concepts of ratios and fractions to solve this problem. We will simplify the ratio in simplest form and define two variables. Then we will form two equations and solve these to get the required value.

Complete step by step answer:
First let us know about ratios.
Ratio:
It is defined as comparison between two or more quantities of the same units. It also tells us how much the first quantity is present in the second quantity.
It is represented as \[a:b\] which means \[a\] units are there for every \[b\] units.
Here, \[a\] is called antecedent and \[b\] is called consequent.
So, now, in the question, it is given that the ratio of boys to girls is \[2:4\] which is equal to \[1:2\].
That means, out of every three members, there are two girls and a boy.
Let the total number of boys present in the class be \[x\] and total numbers of girls present in the class be \[y\].
So, the ratio of boys to girls is \[x:y\] which is equivalent to \[1:2\]
If we write these ratios in fraction form, we get, \[\dfrac{x}{y} = \dfrac{1}{2}\]
On cross multiplying, \[2x = y\] ------(1)
And the class total is equal to 24.
So, the sum of the total number of boys and total number of girls is equal to 24.
\[ \Rightarrow x + y = 24\] -----(2)
From the equation (1), substitute the value of \[y\] in equation (2)
\[ \Rightarrow x + 2x = 24\]
\[ \Rightarrow 3x = 24\]
Divide the whole equation by 3.
\[ \Rightarrow x = \dfrac{{24}}{3} = 8\]
And \[y = 2x\] from equation (1)
So, \[y = 2(8)\]
\[ \Rightarrow y = 16\]
So, finally, there are 8 boys and 16 girls.

Note:
A ratio should always be in a simplified form i.e., it should be reduced to its lowest form. If two ratios are equivalent, then its product of means is equal to its extremes.
Consider \[a:b = c:d\]
Here, \[a{\text{ and }}d\] are called extremes and \[b{\text{ and }}c\] are called means.
So, \[a \times d = b \times c\]