SOLUTION: Alice’s employer withholds from her monthly paycheck $102 for federal and state taxes and retirement. She noticed that the amount withheld for her state income tax is $13 more than

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Alice’s employer withholds from her monthly paycheck $102 for federal and state taxes and retirement. She noticed that the amount withheld for her state income tax is $13 more than      Log On


   

Question 550925: Alice’s employer withholds from her monthly paycheck $102 for federal and state taxes and retirement. She noticed that the amount withheld for her state income tax is $13 more than that withheld for retirement. The amount withheld for federal income tax is three times the amount for the state tax. How much is withheld monthly for federal tax? State tax? Retirement?
Answer by TutorDelphia(193) About Me  (Show Source):
You can put this solution on YOUR website!
We have three unknowns so lets give them variables
federal will be f
state =s
retirement=r
We know the total of f,s and r is 102
f+s+r=102
the amount withheld for her state income tax is $13 more than that withheld for retirement.
s=13+r
The amount withheld for federal income tax is three times the amount for the state tax.
f=3s
Now lets look again at:
f+s+r=102
we can sub in for f
3s+s+r=102
4s+r=102
Now if we sub in again we find for s
4(13+r)+r=102
52+4r+r=102
5r=50
r=10
Going back to s=13+r
s=23
f=3s
f=69