SOLUTION: The sum of the digits of a five-digit palindrome (a number that reads the same way in either direction) is 30. the sum of the first two digits is twice the value of the middle di
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Question 273169: The sum of the digits of a five-digit palindrome (a number that reads the same way in either direction) is 30. the sum of the first two digits is twice the value of the middle digit and the first is twice the second digit . find the palindrome ?
A 48684 b 63636 c 93636 d 75657 e 84648
You can put this solution on YOUR website! 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 =
y = 4
then
x = 2(4) = 8
and
z = 1.5(4) = 6
:
84648 is the number
