SOLUTION: A wealthy man died and left an estate of $975, 240 to be divided among 5 friends, 4 charitable organizations, and his university. His will directed that each friend should receive

Question 414342: A wealthy man died and left an estate of $975, 240 to be divided among 5 friends, 4 charitable organizations, and his university. His will directed that each friend should receive 3 times as much as all the charities combined, and that each charity should receive twice as much as the the university. How much did they all receive?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A wealthy man died and left an estate of $975, 240 to be divided among 5 friends, 4 charitable organizations, and his university. His will directed that each friend should receive 3 times as much as all the charities combined, and that each charity should receive twice as much as the the university. How much did they all receive?
--------------------------------
Let university share be "x".
Then each charity's share is "2x".
And each friend should receive 3(4*2x)) = 24x
-----
Solve: 5*24x + 4(2x) + x = 975240
120x+8x+x = 975240
129x = 975240
x = 7560 (university share)
2x = 15120 (each charity's share)
24x = 24*7560 = 181440 (each friend's share)
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Cheers,
Stan H.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = amount received by each friend
Let = amount received by each charity
Let = amount received by the University
given:
(1)
(2)
(3)
This is 3 equations and 3 unknowns, so it's solvable
----------------
Substitute (3) into (1)
(3)
(1)
Substitute (2) into (1)
(1)

and
(3)

and
(2)

The 5 friends each got $181,440
The 4 charities each got $15,120
The University got $7,560
check answer:
(1)
(1)
(1)
(1)
OK
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