Question

How many 0.45 ounce packages of cinnamon can be made with 3.15 ounces of cinnamon?

Answer 1

Hint: Assume the number of packets of cinnamon that can be made as n. Use the fact that the mass of total cinnamon will remain constant before and after the packaging, so equate the total mass of n number of packets weighing 0.45 ounce each with the total mass of cinnamon present, i.e. 3.15 ounce. Multiply both the sides with 100 to remove the decimal part and cancel the common factors to get the value of n.

Complete step by step solution:
Here we have been provided with 3.15 ounce of cinnamon and asked to make its small packets each of whose weight should be 0.45 ounce. We need to determine the total number of packets that can be made.
Let us assume the total number of cinnamon packets that can be formed is n. Now, since the amount of cinnamon is not changing so we can say that the total weight or mass of the cinnamon will remain constant. Therefore, the total weight of n number of packets will be equal to the total weight of cinnamon present.
$\because $ Since weight of one packet = 0.45 ounce
$\Rightarrow $ Weight of n number of packets = $n\times 0.45$ ounce
$\Rightarrow n\times 0.45=3.15$
Multiplying both the sides with 100 to remove the decimal point we get,
$\Rightarrow n\times 45=315$
Dividing both the sides with 45 and cancelling the common factors we get,
$\begin{align}
  & \Rightarrow n=\dfrac{315}{45} \\
 & \Rightarrow n=7 \\
\end{align}$

Hence, we can make 7 packets of cinnamon.

Note: Here you may notice that this is a basic question of the unitary method. We can also understand it in a different language by saying that if one package of cinnamon weighs 0.45 ounce then 7 packages will weigh 3.15 ounce. Here we do not need to convert the unit ounce into another unit of weight because in the end the units will get cancelled. We have multiplied both the sides with 100 to make our calculation easy.