Dan made $\$ 252$ for 12 hours of work. At the same rate, how many hours would he have to work to make $\$ 105$?

Hint: To solve this question, we first need to find out the earning of Dan in one hour. After obtaining one hour’s earning of Dan, we can calculate the number of working hours required by him to earn the given amount of money. This can be done by simply dividing it by the given amount.

Complete step by step solution:
We are given that Dan worked 12 hours and made $\$ 252$.
Here, we will first determine the money he would earn per hour.
Let us consider that he has made $\$ x$ in one hour and we can find this $x$ by following method:

Therefore, we can say that $x = \dfrac{{1 \times 252}}{{12}} = 21$.
Thus, Dan earned $\$ 21$per hour.
Now, we will determine the number of hours he would have to work to earn $\$ 105$.
Let us consider that Dan would have to work for $y$ hours to make $\$ 105$ and this $y$ can be determined by the following method:


Therefore, we can say that $y = \dfrac{{105 \times 1}}{{21}} = 5$.
Hence, our final answer is: Dan would have to work for 5 hours to make $\$ 105$.
So, the correct answer is “5 hours”.

Note: Here, we have calculated one hour’s earning first and then determined the number of hours required. However, we can also directly find the number of hours using the similar method as follows:



$ \Rightarrow y = \dfrac{{105 \times 12}}{{252}} = 5hours$.