SOLUTION: Hello! Can someone help please? My question is: If you take $20 from the first and put it into the second of three purses, the second would then contain 4 times as much as

Click here to see ALL problems on Equations

Question 39080: Hello!
Can someone help please?
My question is:
If you take $20 from the first and put it into the second of three purses, the second would then contain 4 times as much as remains in the first. If $60 of what is now in the second is put into the third, the third will contain twice what is in the first and second together. Now, if $40 be removed from the third and put into the first, there will be half as much as in the third. What did each purse originally hold?
I know the answer is $50, $100 and $120 but I don't know how to work it out.
Thanks
Marcee
Answer by Paul(988) (Show Source):
You can put this solution on YOUR website!
Let the second one be x
Let the first one be y
Let the third one be z
FIRST EQUATION:
x+20=4(y-20)
x=4y-80-20
x=4y-100 (SUBSITUTION 1)

SECOND EQUATION:
z+60=2(y-20+x+20-60)
z+60=2y-40+2x+40-60
z=2y+2x-120 (SUBSITUTION 2)

THIRD EQUATION:
z-40=2y+80

ALLOW THE SUBSITUTION:
Subsitute for z:
2y+2x-120=2y+80
2x=200
x=100
FROM 1st EQUATION:
x=4y-100

y=50

z=2(50)+2(100)-120
z=180 ( I have no idea how to get 120)
Hence, the money in three purses were $50, $100, and $180.
Paul.