Question

Felicia, Grace, Joan, and Marilyn share a sum of money. Felicia and Grace take 1/3 and 1/4 of the sum of money, respectively. After Felicia and Grace have taken their share, Joan takes 1/5 of the remaining money. After Joan has taken her share, Marilyn takes all of the remaining money. If Marilyn's share is $75, find the original sum of money.

A) $625
B) $750
C) $800
D) $1,000

Answer 1

The original sum of money before any shares were taken is the sum after Felicia and Grace have taken their share, which is $375 + $218.75 = $593.75.

Step-by-step explanation:

To find the original sum of money, we need to work backwards. We know that Marilyn's share is $75 and that she takes all of the remaining money after Joan. So, let's denote the remaining money after Joan as x. Marilyn takes all of the remaining money, which means x is equal to $75. Now, we can work backwards to find the original sum of money.

Joan takes 1/5 of x, so 1/5 of x is equal to $75. Multiplying both sides by 5 gives us x = $375. This means that the sum of money after Felicia and Grace have taken their share is $375.

Grace takes 1/4 of the sum of money, so 1/4 of $375 is equal to $93.75. Adding Felicia's share of 1/3 of the sum of money, which is 1/3 of $375 equal to $125, we get $93.75 + $125 = $218.75.

Therefore, the original sum of money before any shares were taken is the sum after Felicia and Grace have taken their share, which is $375 + $218.75 = $593.75.