Question

Mini observed that 2 butterflies have 12 legs. If she saw 35 butterflies in her garden, then how many legs of butterflies did she see? \[\]
A.182\[\]
B.209\[\]
C.315\[\]
D.210\[\]

Answer 1

Hint: We use the unitary method with direct variation as the number of legs increases with number of butterflies. We find the number of legs of 1 butterfly by dividing 12 by 2 and then multiply the result by 35 to get the total number of legs Mini saw in the garden.

Complete step-by-step answer:
We know that the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. There are two types of two types of unitary method one is direct variation and other is indirect variation. \[\]
When one quality $a$ increases with another quantity $b$ and also $a$ decreases with $b$ the we say the quantities $a$ and $b$ are in direct variation. Here the fraction $\dfrac{a}{b}$ always remains constant. We divide the increasing quantity $a$ by $b$ to obtain the value of single unit and then multiply to find the required value.\[\]

Here in the question that Mini is in the garden and she observed that 2 butterflies have 12 legs. We see that more the number of butterflies more the number of legs and less the number of butterflies less the number of legs. So the problem is in direct variation. Here we have $a=12,b=2$.\[\]
Let us find the number of legs of 1 butterfly by dividing $a$ by $b$. So the number of legs of 1 butterfly is
\[\dfrac{a}{b}=\dfrac{12}{2}=6\]
We are also given in the question that she saw 35 butterflies in her garden. So the total number of legs she saw is
\[35\times \dfrac{a}{b}=35\times 6=210\]
So the correct option is D. \[\]

So, the correct answer is “Option D”.

Note: We need to be careful of the confusion between direct and indirect variation where $a$ decreases with increase in $b$ and $ab$ remains constant. The problems of prices, weights come under direct variation while the problems of speed and time , men and work come under indirect variation.