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

Question 316593: Find a five-digit number in which the first digit equals the sum of the fourth and fifth digits, the second digit equals the sum of the first and third digits, the first digit is one less than the second and the fourth digit is two more than the third. The sum of all the digits is 23.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find a five-digit number in which the first digit equals the sum of the fourth and fifth digits, the second digit equals the sum of the first and third digits, the first digit is one less than the second and the fourth digit is two more than the third. The sum of all the digits is 23.
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Let the number be abcde
Equation:
a = d + e
b = a + c
a = b -1
d = c+2
a + b + c +d + e = 23
------------------------
Rearrange:
a + 0 + 0 - d - e = 0
a - b + c + 0 + 0 = 0
a - b + 0 + 0 + 0 = -1
0 + 0 + c - d + 0 = -2
a + b + c + d + e = 23
-----------------------------
I used a calculator to get:
a = 7
b = 8
c = 1
d = 3
e = 4
================
Cheers,
Stan H.
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Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

============

Substituting what we know so far:

Substituting again:

But since

And finally:

and

The original number is then:

John

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