thinktank wrote:
The majority owner of a business received 25% of the profit, with each of 4 partners receiving 25% of the remaining profit. If the majority owner and two of the owners combined to receive $62,500, how much profit did the business make?
(A) $100,000
(B) $125,000
(C) $150,000
(D) $200,000
(E) $250,000
Call profits P. The majority owner took 0.25*P = P/4 for himself, leaving 0.75*P = 3P/4 for the partners. Each of the four partners took a quarter of this ----- (0.25)*(0.75)*P = 3P/16. (It's a toss up whether it's easier to do this math with fractions or with decimals ---- I'll use decimals.)
Majority owner + two partners = 0.25*P + 2*(0.25)*(0.75)*P = 0.25*P + (0.5)*(0.75)*P = 0.25*P + (0.375)*P = (0.625)*P
This equals $62,500.
(0.625)*P = 62,500 ----- divide both sides by 625
(0.001)*P = 100 ------ multiply by 1000
P = 100,000
Answer =
AI like that it looked like the math was going to be a nightmare, but then because of some fortuitous arrangements, the arithmetic wound up being very easy.
Mike
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)