Question

In a class, the ratio of boys to girls is \[4:3\]. If there are $ 18 $ girls, then find the boys in the class.

Answer 1

Hint: Ratio is defined as the comparison between two numbers without any units Whereas, when the given two ratios are set equal to each other are known as the proportion. Four numbers a, b, c, and d are said to be in the proportion. If $ a:b = c:d $ whereas, four numbers are identified as to be in the continued proportion if the terms are expressed as $ a:b = b:c = c:d $ here we will frame the given data in the mathematical form and will simplify to check the values on both the sides of the equation.

Complete step-by-step answer:
Let us assume the number of boys in the class be “x”
Given that the ratio of boys to girls is \[4:3\] and there are $ 18 $ girls
Frame the ratio and proportions mathematical expression –
 $ \dfrac{x}{{18}} = \dfrac{4}{3} $
Perform cross-multiplication where the numerator of one side is multiplied to the denominator of the opposite side.
 $ \Rightarrow 3x = 4(18) $
Term multiplicative on one side if moved to the opposite side then goes to the denominator.
 $ \Rightarrow x = \dfrac{{4(18)}}{3} $
Find the factors for the numerator in the above expression –
 $ \Rightarrow x = \dfrac{{4 \times 6 \times 3}}{3} $
Common factors from the numerator and the denominator cancels each other and therefore remove
 $ \Rightarrow x = 4 \times 6 $
Simplify the expression finding the product of the term –
 $ \Rightarrow x = 24 $
Hence, there are a total $ 24 $ boys in the class.
So, the correct answer is “ $ 24 $ boys”.

Note: Read the question twice and then frame the equation accordingly. Ratio of the number of girls to boys and boys to girls are two different ratios and frame it wisely and correctly. Common factors from the numerator and the denominator cancel each other, and be good in factorization.