Question

If the ratio of boys to girls is $ 3:2 $ and there are $ 25 $ students in a class, how do you make equal ratios to show how many students in the class are boys and how many are girls?

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.

Complete step by step solution:
Let us consider the common multiple in the given ratios to be “x”.
Therefore, the number of boys $ = 3x $ and
The number of girls $ = 2x $
Now, given that there are a total $ 25 $ students.
 $ 3x + 2x = 25 $
Simplify the above expression –
 $ 5x = 25 $
Term multiplicative on one side, if moved to the opposite side then it goes to the denominator.
 $ x = \dfrac{{25}}{5} $
Find the factors for the term on the numerator.
 $ x = \dfrac{{5 \times 5}}{5} $
Common factors from the numerator and the denominator cancels each other. Therefore, remove from the numerator and the denominator.
 $ \Rightarrow x = 5 $
Hence, the number of boys $ = 3x = 3(5) = 15 $ and
The number of girls $ = 2x = 2(5) = 10 $
Now, the equivalent ratio is $ 15:10 $
So, the correct answer is “ $ 15:10 $ ”.

Note: 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 $