Question

A boutique sold $\$127.50$ worth of purses. Each purse is $\$7.50.$How many purses did they sell?

Answer 1

Hint: We know that if the price of $n$ items is $x,$ then the price of one item or each item is obtained by $\dfrac{x}{n}.$ So, if we are given with the price of a number of objects and the price of each of the objects, then the number of objects can be found by dividing the total price with the price of one object.

Complete step by step solution:
Let us consider the given problem.
We need to find the number of purses sold by the boutique when they obtained a total of $\$127.50$ for selling the purses and one purse is worth $\$7.50.$
Suppose that the boutique sold $n$ number of purses to obtain a total of $\$127.50$ when the price of each purse is $\$7.50.$
Suppose that we are given with the total amount of the objects and the number of objects for which the amount is obtained.
Let the number be $m$ and the total amount obtained be $p.$ Then the amount of one object can be obtained by $q=\dfrac{p}{m}.$ We divided the total amount by the number of objects sold.
We know that if the number is what we want to find, then we should transpose $q$ and $m$ in the above equation. So, we will get $m=\dfrac{p}{q}.$
This is the situation we are dealing with now. We need to find the number of purses sold.
So, we will get \[n=\dfrac{\$127.50}{\$7.50}.\]
We will get $n=17.$
Hence the number of purses sold is $n=17.$

Note: We use division when we need to find the price of one object when we are given with the price of a number of objects. Mathematics provides a great way to deal with different terminologies using the same equations. We just need to transpose the terms accordingly.