SOLUTION: Bill has twice as much money as Jim and half as much as Sue how much does each person have if together they have $120? Need step by step answer. Thank you

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Question 1005763: Bill has twice as much money as Jim and half as much as Sue how much does each person have if together they have $120?
Need step by step answer.
Thank you
Found 2 solutions by fractalier, josmiceli:
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Call their amounts b, j and s.
We have
b + j + s = 120
and
b = 2j or j = (1/2)b
and
b = (1/2)s or s = 2b
Plug these into the first equation and get
b + (1/2)b + 2b = 120
(7/2)b = 120
Now multiply by 2/7 and get
b = 240/7 dollars
j is half that or 120/7 dollars
s is double that or 480/7 dollars

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +b+ = amount that Bill has
Let +j+ = amount that Jim has
Let +s+ = amount that Sue has
----------------------------
(1) +b+=+2j+
(2) +b+=+s%2F2+
(3) +b+%2B+j+%2B+s+=+120+
---------------------
There are 3 unknowns and 3 equations,
so it is solvable
----------------
From (1):
(1) +j+=+b%2F2+
From (2):
(2) +s+=+2b+
----------------
Substitute (1) and (2) into (3)
(3) +b+%2B+j+%2B+s+=+120+
(3) +b+%2Bb%2F2+%2B+2b+=+120+
(3) +%287%2F2%29%2Ab+=+120+
(3) +b+=+%282%2F7%29%2A120+
(3) +b+=+34.29+
and, since:
(1) +j+=+b%2F2+
(1) +j+=+34.29%2F2+
(1) +j+=+17.15+
also:
(2) +s+=+2b+
(2) +s+=+2%2A34.29+
(2) +s+=+68.58+
-------------------
Bill has $34.29
Jim has $17.15
Sue has $68.58
---------------
check:
(3) +b+%2B+j+%2B+s+=+120+
(3) +34.29+%2B17.15+%2B+68.58+=+120+
(3) +120.02+=+120+ ( error due to rounding off )