SOLUTION: Find a five digit number in which the second and fourth digits are the same, the third digit is the sum of the first and second, the fifth digit is the sum of the third and fourth

Question 170677: Find a five digit number in which the second and fourth digits are the same, the third digit is the sum of the first and second, the fifth digit is the sum of the third and fourth and the third digit is one more than the first and one less than the fifth. The sum of all the digits is 14.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find a five digit number in which the second and fourth digits are the same,
ABCBE
:
the third digit is the sum of the first and second,
C = A+B
:
the fifth digit is the sum of the third and fourth
E = C + B
:
the third digit is one more than the first
C = A + 1
A = C - 1
:
Also the third digit is one less than the fifth.
C = E - 1
E = C + 1
;
The sum of all the digits is 14.
A + B + C + B + E = 14
A + 2B + C + E = 14
:
Looking at our equations we see:
E = C + B
And
E = C + 1
Therefore
B = 1
:
Substituting 1 for B in the Sum equation
A + 2(1) + C + E = 14
A + C + E = 14 - 2
A + C + E = 12
:
Substitute (C-1) for A, and (C+1) for E, find C
(C-1) + C + (C+1) = 12
3C = 12
C = 4
Then
A = 4 - 1
A = 3
and
E = 4 + 1
E = 5
:
Our number is: 31415
:
:
Check solution:
the third digit is the sum of the first and second,
4 = 3 + 1
:
the fifth digit is the sum of the third and fourth
5 = 4 + 1
:
and the third digit is one more than the first and one less than the fifth.
4 = 3 + 1
:
The sum of all the digits is 14.
3 + 1 + 4 + 1 + 5 = 14
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