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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?

Respuesta :

let dan's age be x  then:-
 james age is 3x  and  2(x + 3x) is Pauls age so we have:-

x + 3x + 2*4x = 120

12x = 120
x = 10 

so Dans age is 10 , James's age is 30 and Paul's age = 80




boffeemadrid

The ages of James, Paul and Dan is required.

James is 30 years old, Paul is 80 years old and Dan is 10 years old.

Let the ages of James be [tex]j[/tex], Paul be [tex]p[/tex] and Dan be [tex]j[/tex].

James is three times the age of Dan

[tex]j=3d[/tex]

Paul is two times the sum of the ages of James and Dan

[tex]p=2(j+d)\\\Rightarrow p=2(3d+d)\\\Rightarrow p=2(4d)=8d[/tex]

The combined ages of the people is 120

[tex]j+p+d=3d+8d+d\\\Rightarrow 120=12d\\\Rightarrow d=\dfrac{120}{12}\\\Rightarrow d=10[/tex]

[tex]j=3d=3\times 10\\\Rightarrow j=30[/tex]

[tex]p=8d=8\times 10\\\Rightarrow p=80[/tex]

So, James is 30 years old, Paul is 80 years old and Dan is 10 years old.

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