The sum of three numbers is 78. The second number is 2 times the third. The third number is 6 more than the first. What are the numbers?

X+y+z=78

y = 2z

z=x+6

We can express x and y from 2nd and 3d equations, and substitute their values into the 1st.

y = 2z and x = z-6

x+y+z=78

z-6+2z+z=78

4z - 6 = 78

4z = 84

z=21

y = 2z, y=2*21, y=42

x = z-6, x = 21-6, x=15

Answer: x=15, y=42, z=21.

Check:

15+42+21 = 78

78=78