SOLUTION: Mrs. Sterling's will states that three fourths of her estate will be left to her son and $24,000 will go to her niece. Half of the remainder will got to her church. One third of th

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Mrs. Sterling's will states that three fourths of her estate will be left to her son and $24,000 will go to her niece. Half of the remainder will got to her church. One third of th      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 193184: Mrs. Sterling's will states that three fourths of her estate will be left to her son and $24,000 will go to her niece. Half of the remainder will got to her church. One third of the money remaining after the church donation will go to her alma mater and the remaining $4000 will pay for Mrs. Sterling's attorney. How much is Mrs. Sterling's estate worth?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Mrs. Sterling's will states that three fourths of her estate will be left to
her son and $24,000 will go to her niece. Half of the remainder will got to
her church. One third of the money remaining after the church donation will
go to her alma mater and the remaining $4000 will pay for Mrs. Sterling's attorney.
How much is Mrs. Sterling's estate worth
:
Let x = total amt of the estate
;
x = .75x + 24000 + .5(x-.75x-24000) + 1%2F3*.5(x-.75x-24000) + 4000
:
x = .75x + 24000 + .5(.25x-24000) + 1%2F3*.5(.25x-24000) + 4000
:
x = .75x + 24000 + .125x - 12000 + 1%2F3*(.125x-12000) + 4000
Group like terms
x = .75x + .125x + 24000 - 12000 + 4000 +1%2F3(.125x-12000)
:
x = .875x + 16000 + 1%2F3(.125x-12000)
Multiply equation by 3
3x = 2.625x + 48000 + .125x - 12000
:
3x = 2.625x + .125x + 48000 - 12000
;
3x = 2.75x + 36000
:
3x - 2.75x = 36000
:
.25x = 36000
x = 36000%2F.25
x = 144,000 is the value of the estate
:
:
Check each heir's amt:
Son = 108000
niece= 24000
church= 6000
almama= 2000
lawyer= 4000
-------------
total 144,000