SOLUTION: I need help setting up a linear system from a word problem. Here it is: A father plans to distribute his estate, worth $234,000, among his four daughter as follows: 2/3 of the

Question 261844: I need help setting up a linear system from a word problem. Here it is:
A father plans to distribute his estate, worth $234,000, among his four daughter as follows: 2/3 of the estate is to be split equally among the daughters. For the rest, each daughter is to receive $3,000 for each year that remains until her 21st birthday. Given that the daughters are each 3 years apart, how much would each receive from her father's estate? How old are the daughters now?
Any help would be greatly appreciated.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A father plans to distribute his estate, worth $234,000, among his four daughter as follows:
2/3 of the estate is to be split equally among the daughters.
For the rest, each daughter is to receive $3,000 for each year that remains until her 21st birthday.
Given that the daughters are each 3 years apart, how much would each receive from her father's estate?
How old are the daughters now?
:
Calculate how much each daughter gets initially
d =
d = 39,000 to each intially
:
The remaining 1/3
*234000 = $78,000
:
"For the rest, each daughter is to receive $3,000 for each year that remains until her 21st birthday.Given that the daughters are each 3 years apart, how much would each receive from her father's estate?"
Let x = youngest daughter's age
then
(x+3) = 2nd daughter
(x+6) = 3rd one
(x+9) = 4th one
:
Subtract each one's age from 21, multiply by 3000
3000[(21-x) + (21 -(x+3)) + (21 - (x+6)) + (21 - (x+9))] = 78000
:
Combine like terms
3000(84 - 4x - 18) = 78000
3000(66 - 4x) = 78000
:
Divide both sides by 3000
66 - 4x = 26
66 - 26 = 4x
x =
x = 10 yrs is the youngest daughter's age (11 yrs from 21st birthday)
then
Youngest daughter receives, 39000 + 11(3000) = $72,000
:
2nd daughter = 13 yrs; receives, 39000 + 8(3000) = $63,000
:
3rd daughter = 16 yrs; receives, 39000 + 5(3000) = $54,000
:
4th daughter = 19 yrs; receives, 39000 + 2(3000) = $45,000
-----------------------------------------------------------
Check solutions by adding all the inheritances = $234,000
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