Question

Santa received 7/10 of the profits on the goods he sold. He gave 5/6 of what he received to Mrs. Claus, and she gave 1/7 of that amount to the elf. What fraction of the total profits did the elf receive?

Answer 1

Given:

Amount of profit received = 7/10

Amount he gave to Mrs. Claus = 5/6

Amount she gave to the elf = 1/7 of the amount Mrs. Claus received.

Let's find the fraction of total profits the elf received.

Let's first find the fraction of profit Mrs. Claus received.

We have:

`\begin{gathered} (5)/(6)*(7)/(10) \\ \\ =(5*7)/(6*10) \\ \\ =(35)/(60) \\ \\ =(7)/(12) \end{gathered}`

Now, since the elf received 1/7 of the amount Mrs. Claus received, the total of profits the elf received will be:

`\begin{gathered} (1)/(7)*(7)/(12) \\ \\ =(1*7)/(7*12) \\ \\ =(1)/(12) \end{gathered}`

Therefore, the fraction of the total profits the elf received is 1/12.

ANSWER:

`(1)/(12)`