Question

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?
Dan is ___ years old
James is ___ years old
Paul is ____ years old.

Answer 1

Answer:

Step-by-step explanation:

From the problem statement, we can create the following equation:

$J + P + D = 120$

where $J$ is the age of James, $P$ is the age of Paul, and $D$ is the age of Dan.

From the first part of the second sentence, we can set up the following equation:

$J = 3D$

From the last part of the second sentence, we can set up the following equation:

$P = 2(J + D)$

We can substitute the second equation into the last one to get the following:

$P = 2(3D + D)$

$P = 2(4D)$

$P = 8D$

We can then substitute the last two equations in the first to solve for $D$:

$3D + 8D + D = 120$

$12D = 120$

$D = 10$

Plugging this into the other two equations will give us the remaining ages:

$P = 8D$

$P = 8(10)$

$P = 80$

$J = 3D$

$J = 3(10)$

$J = 30$