Answer:
Step-by-step explanation:
From the problem statement, we can create the following equation:
[tex]J + P + D = 120[/tex]
where [tex]J[/tex] is the age of James, [tex]P[/tex] is the age of Paul, and [tex]D[/tex] is the age of Dan.
From the first part of the second sentence, we can set up the following equation:
[tex]J = 3D[/tex]
From the last part of the second sentence, we can set up the following equation:
[tex]P = 2(J + D)[/tex]
We can substitute the second equation into the last one to get the following:
[tex]P = 2(3D + D)[/tex]
[tex]P = 2(4D)[/tex]
[tex]P = 8D[/tex]
We can then substitute the last two equations in the first to solve for [tex]D[/tex]:
[tex]3D + 8D + D = 120[/tex]
[tex]12D = 120[/tex]
[tex]D = 10[/tex]
Plugging this into the other two equations will give us the remaining ages:
[tex]P = 8D[/tex]
[tex]P = 8(10)[/tex]
[tex]P = 80[/tex]
[tex]J = 3D[/tex]
[tex]J = 3(10)[/tex]
[tex]J = 30[/tex]
