# math

i am a number less than 10.my hundreds digit is 3 more than my thousands digit,my tenths is 2 less than my hundreds and my ones is the sum of my tenths and hundreds digits.what number can i be?

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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

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