SOLUTION: Every digit is different. The sum of the thousands digit and the tens is 10. The sum of all the digits is 16. The difference between the hundreds digit and the ones digit is 6. The

Question 563225: Every digit is different. The sum of the thousands digit and the tens is 10. The sum of all the digits is 16. The difference between the hundreds digit and the ones digit is 6. The difference between the thousands digit and the hundreds digit is 3. The number is greater than 8,000.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Every digit is different: a, b, c, d
;
We are going to try and get everything in terms of b
:
The sum of the thousands digit and the tens is 10.
a + c = 10
:
The sum of all the digits is 16.
a + b + c + d = 16
:
The difference between the hundreds digit and the ones digit is 6.
b - d = 6
b - 6 = d
d = (b-6)
:
The difference between the thousands digit and the hundreds digit is 3.
a - b = 3
a = (b+3)
:
In the 1st equation, replace a with (b+3)
(b+3) + c = 10
c = 10 - (b+3)
c = -b + 7
:
Replace a, c, d in the 2nd equation a+b+c+d = 16
(b+3) + b + (-b+7) + (b-6) = 16
combine like terms
2b + 4 = 16
2b = 16 - 4
2b = 12
b = 6
:
Then
a = 6 + 3
a = 9
and
c = -6 + 7
c = 1
and
d = 6 - 6
d = 0
:
The number: 9610

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