Question

The ratio of boys to girls in the science club is $ 3:5. $ If there are $ 60 $ girls, how many boys are there?

Answer 1

Hint: Identify the known and unknown ratios and set up the ratio and proportion and solve accordingly. In these ratio and proportion types of questions, take any variable as the reference number where applicable and frame the word statements in to the form of mathematical expressions.

Complete step-by-step answer:
Let us suppose the number of boys be equal to “x”
Let us frame the given word statements in the form of fractional form.
\[ \Rightarrow \dfrac{3}{5} = \dfrac{x}{{60}}\]
Perform cross multiplication in the above expression where the numerator of one side is multiplied with the denominator of the opposite side.
 $ \Rightarrow 3 \times 60 = 5x $
The above equation can be re-written as –
 $ \Rightarrow 5x = 3 \times 60 $
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
 $ \Rightarrow x = \dfrac{{3 \times 60}}{5} $
Find the factors from on the numerator of the above expression.
 $ \Rightarrow x = \dfrac{{3 \times 12 \times 5}}{5} $
Common factors from the numerator and the denominator cancel each other.
 $
   \Rightarrow x = 3 \times 12 \\
   \Rightarrow x = 36 \;
  $
Hence, there are $ 36 $ boys in the science club.
So, the correct answer is “$ 36 $ boys”.

Note: Always read the question twice and frame the word statement in the mathematical form. Segregate all the known and unknown terms and form the corresponding ratios and the proportions accordingly.
Ratio is the comparison between two numbers without any units.
Whereas, when two ratios are set equal to each other are called 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 said to be in continued proportion if the terms \[\] $ a:b = b:c = c:d $