Question 563225
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