Question

The weight of four boxes of biscuits is $36\;$ ounces. How many ounces can nine boxes weigh?

Answer 1

Hint: To solve these types of questions, the concept of direct proportion can be applied. In this method, the two quantities x, y in direct proportion can be expressed as $\dfrac{a}{b}=k$ where k is any constant. Then, we cross multiply the terms and simplify them to get the required result.

Complete step by step answer:
We are given the weight of four boxes of biscuits as 36 ounces and need to find the weight of nine boxes. We will be solving the given question using the concept of direct proportion.
Let us consider the weight of nine boxes of biscuits in ounces as $x$ .
Using the concept of direct proportion, we can form the equation to find the weight of nine boxes of biscuits as follows,
$\Rightarrow \dfrac{4}{36}=\dfrac{9}{x}$
Cross multiplying the above terms, we will get,
$\Rightarrow 4\times x=9\times 36$
Multiplying the terms together we get,
$\Rightarrow 4x=324$
Now, let us divide both the sides of the equation by the number $4$ , to get,
$\Rightarrow \dfrac{4x}{4}=\dfrac{324}{4}$
Simplifying the above equation, we get,
$\Rightarrow x=\dfrac{324}{4}$
$\therefore x=81$

Therefore, the value of $x$ is $81\;$ which we assumed to be the weight of nine boxes of biscuits in the starting of our solution.

Note: The above question can be alternatively solved by using the concept of unitary method as follows,
The weight of four boxes of biscuits: $36\;$ ounces
Therefore, the weight of one box of biscuit will be,
$\Rightarrow \dfrac{36}{4}=9$ ounces.
Now, we need to calculate the weight of similar nine boxes of biscuits
For the same, we need to multiply the weight of one box of biscuit with the total number of boxes of biscuits whose weight we have to find out, to get,
Weight of nine boxes of biscuits in ounces $=\;$ number of boxes of biscuits $\times$ weight of one box of biscuit
$\Rightarrow 9\times 9=81$
The nine boxes of biscuits weigh $81\;$ ounces.