SOLUTION: A palindrome is a number that reads the same forwards and backwards. The sum of a particular set of three consecutive positive integers is a three-digit palindrome. If the sum is l

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Question 217724: A palindrome is a number that reads the same forwards and backwards. The sum of a particular set of three consecutive positive integers is a three-digit palindrome. If the sum is less than 220, what is the greatest possible value for the largest of the three integers in the set?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
palindrome is a number that reads the same forwards and backwards.
The sum of a particular set of three consecutive positive integers is a three-digit palindrome.
If the sum is less than 220, what is the greatest possible value for the largest of the three integers in the set?
:
Less than 220 therefore the number is 212 or the 1st and 3rd digit = 1
I tried 212, does not have an integer solution.
Let the 1st and 3rd digit = 1
Let the middle digit = x
Let consecutive integers = y, y+1, y+2
:
y + (y+1) + (y+2) = 100 + 10x + 1
;
combine like terms
3y + 3 = 10x + 101
;
3y = 10x + 101 - 3
;
3y = 10x + 98
y = %2810x%2B98%29%2F3
:
Find a value for x that will give an integer value for y
The sum of the numerator has to be a multiply of 3
x = 7
y = %2810%287%29%2B98%29%2F3
y = %28168%29%2F3
y = 56
:
Try this
56 + 57 + 58 = 171, satisfies the problem