<PRE><B>Question 273169</B>
Let x = 1st and last digit
Let y = 2nd and 4th digit
Let z = middle digit
:
x,y,z,y,x is the 5 digit number
:
The sum of the digits of a five-digit palindrome is 30.
2x + 2y + z = 30
:
the sum of the first two digits is twice the value of the middle digit
x + y = 2z
:
the first is twice the second digit
x = 2y
:
find the palindrome ? 
x + y = 2z
2z = x + y
2z = 2y + y; replaced x with 2y
2z = 3y
z = 1.5y
:
2x + 2y + z = 30
2(2y) + 2y + 1.5y = 30, replaced x and z
4y + 2y + 1.5y = 30
7.5y = 30
y = {{{30/7.5}}} 
y = 4
then
x = 2(4) = 8
and
z = 1.5(4) = 6
:
84648 is the number</PRE>