# math

posted by on .

i am a three digit number. my hundreds digit is three more than my ones digit.my tens digit is oneless than my hundreds digit. what numbers can i be?

• math - ,

d = 100 x + 10 y + z

my hundreds digit is three more than my ones

x = z + 3

that is equivalent with :

z = x - 3

my tens digit is oneless than my hundreds

y = x - 1

d = 100 x + 10 y + z

d = 100 * x + 10 * ( x - 1 ) + x - 3

d = 100 x + 10 x - 10 + x - 3 = 111 x - 13

Solution 1 :

x = 9

y = x - 1 = 9 - 1 = 8

z = x - 3 = 9 - 3 = 6

d = 986

Solution 2 :

x = 8

y = x - 1 = 8 - 1 = 7

z = x - 3 = 8 - 3 = 5

d = 875

Solution 3 :

x = 7

y = x - 1 = 7 - 1 = 6

z = x - 3 = 7 - 3 = 4

d = 764

Solution 4 :

x = 6

y = x - 1 = 6 - 1 = 5

z = x - 3 = 6 - 3 = 3

d = 653

Solution 5 :

x = 5

y = x - 1 = 5 - 1 = 4

z = x - 3 = 5 - 3 = 2

d = 542

Solution 6 :

x = 4

y = x - 1 = 4 - 1 = 3

z = x - 3 = 4 - 3 = 1

d = 431

Solution 7 :

x = 3

y = x - 1 = 3 - 1 = 2

z = x - 3 = 3 - 3 = 0

d = 320

• math - ,

Just start by putting 0, 1,2, ... into the ones digit
then fulfilling the other two conditions
320
431
542
653
764
875
986 , can't use 7 or higher for the unit digits