Posted by joshua on Thursday, August 23, 2012 at 11:08pm.
n = your number
a = ones digit
b = tenths digin
c = hundreds digit
d = thousands digit
n = a + b / 10 + c / 100 + d / 1000
c = d + 3
b = c - 2 = d + 3 - 2 = d + 1
a = b + c = d + 1 + d + 3 = 2 d + 4
n = a + b / 10 + c / 100 + d / 1000
n = 2 d + 4 + ( d + 1 ) / 10 + ( d + 3 ) / 100 + d / 1000 Multiply both sides by 1000
1000 n = 1000 * ( 2 d + 4 ) + 1000 * ( d + 1 ) / 10 + 1000 * ( d + 3 ) / 100 + 1000 * d / 1000
1000 n = 1000 * ( 2 d + 4 ) + 100 * ( d + 1 ) + 10 * ( d + 3 ) + d
1000 n = 2000 d + 4000 + 100 d + 100 + 10 d + 30 + d
1000 n = 2111 d + 4130
For d = 0
1000 n = 2111 * 0 + 4130
1000 n = 0 + 4130 = 4130 Divide both sides by 1000
n = 4.130
For d = 1
1000 n = 2111 * 1 + 4130
1000 n = 2111 + 4130 = 6241 Divide both sides by 1000
n = 6.241
For d = 2
1000 n = 2111 * 2 + 4130
1000 n = 4222 + 4130 = 8352 Divide both sides by 1000
n = 8.352
For d = 3
1000 n = 2111 * 3 + 4130
1000 n = 6333 + 4130 = 10463 Divide both sides by 1000
n = 10.463
A number must be less than 10 , so that is not solution.
For d = 3 , 4 , 5 ... n > 10
The solutions are :
n = 4.130
n = 6.241
n = 8.352