SOLUTION: The combined age of three relatives is 120 years. James is three times the age of Dan, and Paul is two times the sum of the ages of James and Dan. How old is each person?

Question 1009242: The combined age of three relatives is 120 years. James is three times the age of Dan, and Paul is two times the sum of the ages of James and Dan. How old is each person?
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
Set J = age of James, D = age of Dan, P = age of Paul
J + D + P = 120 , combined ages
J = 3D , James is three times the age of Dan
P = 2(J + D) , Paul is 2 times the sum of James and Dan
Since J = 3D , J - 3D = 0
P = 2(J + D) -- P = 2J + 2D so
2J + 2D - P = 0
We now have three revised equations
J + D + P = 120
J - 3D = 0
2J + 2D - P = 0
Substitute 3D for J in J + D + P = 120
3D + D + P = 120
4D + P = 120
add -4D to each side
P = 120 - 4D
Now substitute (120 - 4D) for P, and 3D for J in P = 2(J + D)
(120 - 4D) = 2(3D + D)
120 - 4D = 2(4D)
120 - 4D = 8D
add 4D to each side
120 = 8D +4D
120 = 12D
Divide each side by 12
10 = D
Since J = 3D, J = 3(10) = 30
Substitute 10 for D and 30 for J in J + D + P = 120
30 + 10 + P = 120
40 + P = 120
add -40 to each side
P = 80
So James is 30, Dan is 10, and Paul is 80

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