The sum of three numbers is
102
. the third number is
2
times the second. the first number is
6
more than the second. what are the numbers?

X+y+z=102
z is 2 times 2nd
z=2y
first is 6 more than 2nd
x=6+y
sub those

6+y+y+2y=102
6+4y=102
minus 6 both sides
4y=96
divide by 4
y=24
sub
z=2y
z=2(24)
z=48

x=6+y
x=6+24
x=30

they are
30, 24, 48

Let the first number be x, the second be y, and the third be z.
x + y + z = 102

The third number is 2 times the second, so z = 2y
The first number is 6 more than the second, so x = y + 6

We replace each letter by it's y value:
y + 6 + y + 2y = 102
4y + 6 = 102
4y = 96
y = 24

As we stated before, z = 2y = 2*24 = 48
And x = y + 6 = 24 + 6 = 30

So, we get x = 30, y = 24, z = 48
x + y + z = 102
30 + 24 + 48 = 102

Hope this Helps! :D