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Metropolis Corporation has 4 shareholders: Fritz, Luis, Alfred and Werner. Number of shares that Fritz owns is \(\frac{2}{3}\) of number of the shares of the other three shareholders, number of the shares that Luis owns is \(\frac{3}{7}\) of number of the shares of the other three shareholders and number of the shares that Alfred owns is \(\frac{4}{11}\) of number of the shares of the other three shareholders. If dividends of $3,600,000 were distributed among the 4 shareholders, how much of this amount did Werner receive?

A. $90,000 B. $100,000 C. $120,000 D. $180,000 E. $240,000

Metropolis Corporation has 4 shareholders: Fritz, Luis, Alfred and Werner. Number of shares that Fritz owns is \(\frac{2}{3}\) of number of the shares of the other three shareholders, number of the shares that Luis owns is \(\frac{3}{7}\) of number of the shares of the other three shareholders and number of the shares that Alfred owns is \(\frac{4}{11}\) of number of the shares of the other three shareholders. If dividends of $3,600,000 were distributed among the 4 shareholders, how much of this amount did Werner receive?

A. $90,000 B. $100,000 C. $120,000 D. $180,000 E. $240,000

Fritz owns \(\frac{2}{3}\) of the shares of the other three shareholders: Fritz owns \(\frac{2}{2+3}=\frac{2}{5}\) of all shares;

Luis owns \(\frac{3}{7}\) of the shares of the other three shareholders: Luis owns \(\frac{3}{3+7}=\frac{3}{10}\) of all shares;

Alfred owns \(\frac{4}{11}\) of the shares of the other three shareholders: Alfred owns \(\frac{4}{4+11}=\frac{4}{15}\) of all shares;

Together these three own \(\frac{2}{5}+\frac{3}{10}+\frac{4}{15}=\frac{29}{30}\) of all shares, which means that Werner owns \(1-\frac{29}{30}=\frac{1}{30}\). Hence from $3,600,000 Werner gets \($3,600,000*\frac{1}{30}=$120,000\).

How do you get the fraction 2/5th's of the total out of 2/3rd's of the shares of the other 3? Like why do you do 2/2+3? I can't seem to figure out how that computes.... thank you

How do you get the fraction 2/5th's of the total out of 2/3rd's of the shares of the other 3? Like why do you do 2/2+3? I can't seem to figure out how that computes.... thank you

It's quite simple: A has $2 and B has 3$ --> A has 2/3rd of B's amount and also 2/(2+3)=2/5th of total amount of $5.

How do you get the fraction 2/5th's of the total out of 2/3rd's of the shares of the other 3? Like why do you do 2/2+3? I can't seem to figure out how that computes.... thank you

It's quite simple: A has $2 and B has 3$ --> A has 2/3rd of B's amount and also 2/(2+3)=2/5th of total amount of $5.

even i have the same doubt "How do you get the fraction 2/5th's of the total out of 2/3rd's of the shares of the other 3? Like why do you do 2/2+3? I can't seem to figure out how that computes."

i did not understand the solution posted above please explain a little more in detail.

even i have the same doubt "How do you get the fraction 2/5th's of the total out of 2/3rd's of the shares of the other 3? Like why do you do 2/2+3? I can't seem to figure out how that computes."

i did not understand the solution posted above please explain a little more in detail.

For those who are still confused. F=2/3 of (1-F) F=2/3-2F/3 3F=2-2F 5F=2 hence, F=2/5 This is a longer method and not advised during the exam, just for clarity

I think this the explanation isn't clear enough, please elaborate. Please explain solution in detail. How did you arrive that own share of Fritz is 2/2+3=2/5 pf all??

I think this the explanation isn't clear enough, please elaborate. Please explain solution in detail. How did you arrive that own share of Fritz is 2/2+3=2/5 pf all??

Other solution: I think you can treat this problem as a ratio problem:

Number of shares that Fritz owns is \(\frac{2}{3}\) of number of the shares of the other three shareholders. That means: F=\(\frac{2}{3}\)(L+A+W). We can re-write this as \(\frac{F}{L+A+W}\)=\(\frac{2}{3}\). So, the ratio of F to (L+A+W) to Total (=F+L+A+W) is 2:3:5. That means \(\frac{F}{Total}\)=\(\frac{2}{5}\) <=> F=\(\frac{2}{5}\)Total

The same for the others Please correct me if i'm wrong.

For those who are still confused. F=2/3 of (1-F) F=2/3-2F/3 3F=2-2F 5F=2 hence, F=2/5 This is a longer method and not advised during the exam, just for clarity

Thanks for this explanation. I think the confusion stems from how the question is worded. It's clear once you take 2/3 of (1-F).