Question

Loki, Moe, Nick and Ott are good friends. Ott had no money, but the others did. Moe gave Ott one-fifth of his money, Loki gave Ott one-fourth of his money and Nick gave Ott one-third of his money. Each gave Ott the same amount of money. What fractional part of the group's money does Ott now have

Answer 1

Explanation:

x = Moe's money

y = Loki's money

z = Nick's money

1/5 x = 1/4 y = 1/3 z (Moe gave 1/5, Loki 1/4, Nick 1/3, but all donations to Ott are the same amount of money).

that also means

y = 4/5 x

z = 3/5 x

in total the group has

x + 4/5 x + 3/5 x = 5/5 x + 4/5 x + 3/5 x = 12/5 x

Ott got 3× 1/5 x (since everybody gave the same amount of money, so it is in sum 3 times of what Moe gave).

so, Ott now has 3/5 x , out of a total of 12/5 x.

his fractional part is therefore

3/5 / 12/5 = 3/5 × 5/12 = 3/12 = 1/4.

he has 1/4 of the group's total money.