Question

A dime weighs about $\dfrac{1}{12}$ ounce. Jody has $1$ pound ( $16$ ounces) of dimes. About how many dimes does she have?

Answer 1

Hint: This problem incorporates the utilisation of the unitary method to the fullest. At first, we find out $1$ ounce is the weight of how many dimes and then from this, find out $16$ ounces is the weight of how many dimes. In this way, after applying the unitary method, we find the answer to be $192$ dimes.

Complete step-by-step solution:
The weight of a dime is given as $\dfrac{1}{12}$ ounce. Now, Jody has $1$ pound of dimes. We know and also it is given that $1$ pound is equal to $16$ ounces. Now, the unitary method comes into play. Unitary method is a simple way to scale or descale a conversion. For example, if one book has $1200$ pages, we can find out how many pages there are in $16$ books and vice-versa. So, rephrasing the problem in the unitary method style, we write,
$\dfrac{1}{12}$ ounce is the weight of $1$ dime.
$\Rightarrow 1$ ounce is the weight of $\dfrac{1}{\dfrac{1}{12}}$ dime or $12$ dimes.
$\Rightarrow 16$ ounces is the weight of $\left( 12\times 16 \right)$ dimes or $192$ dimes.
But, $16$ ounces is nothing but $1$ pound.
Therefore, we can conclude that Jody has $192$ dimes.

Note: We should be careful while executing the unitary method as the process involves the operation of fractions. The problem can also be solved in a slightly different approach. The weight of a dime is given as $\dfrac{1}{12}$ ounce. In a reverse way, we can say that $\dfrac{1}{12}$ ounce is the weight of one dime. Thus, $1$ ounce is the weight of $12$ dimes, which can be done simply by using the unitary method. Now, it is said that Jody has $1$ pound of dimes. We know and also it is given that $1$ pound is equal to $16$ ounces. Now, the unitary method comes into play. We have seen how $1$ ounce in the weight of $12$ dimes. So, $16$ ounces is the weight of $\left( 12\times 16 \right)$ which is equal to $192$ dimes.