Question

How many packages of diapers can you buy with $\$ 40$ if one package costs $\$ 8$?

Answer 1

Hint: To solve this question, we need to use the unitary method. We will divide the given money by the cost of one packet to get the required number of packages of diapers. The unitary method is the method in which we first find the cost of 1 unit, then using it we find the cost of the required number of units.

Complete step-by-step solution:
According to the question, the cost of one package is equal to $\$ 8$. We can also say this as with the cost of $\$ 8$, we can buy one package.
This implies that with the cost of $\$ 1$, the number of packages obtainable is $\dfrac{1}{8}$.
Finally, using the unitary method, the number of packages obtainable with the cost of $\$ 40$ will be equal to $40$ times that number of packages obtainable with the cost of $\$ 1$. Therefore, the number of packages of diapers which can be bought with $\$ 40$ is given by
$n = 40 \times \dfrac{1}{8}$
$ \Rightarrow n = 5$

Hence, the number of packages we can buy with $\$ 40$ is equal to $5$.

Note:
The number of packages obtainable with $\$ 1$ is found to be equal to $\dfrac{1}{8}$, which is determined by the unitary method. This seems absurd, as the number of packages cannot be fractional. But we must not worry about this absurdity, as the unitary method will always give the correct result. For using the unitary method, we must know the cost of 1 unit of an item. If we are not provided with the cost of 1 unit, then we will find it by dividing the price by the number of units.