SOLUTION: what 4 digit number becomes 9x the original number when read backwards

Question 623345: what 4 digit number becomes 9x the original number when read backwards
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
what 4 digit number becomes 9x the original number when read backwards
:
From the information given, we know that 1st digit has to be 1,
then the last digit had to be 9*1 = 9
:
1st original digit = 1 (thousands)
let a = 2nd original digit (100's)
let b = 3rd original digit (10's)
last original digit = 9 (units)
:
Nine times original number = reversed number
:
9(1000 + 100a + 10b + 9) = 9000 + 100b + 10a + 1
9000 + 900a + 90b + 81 = 9000 + 100b + 10a + 1
combine like terms
900a + 90b + 9081 = 100b + 10a + 9001
900a - 10a + 90b - 100b + 9081 - 9001 = 0
890a - 10b + 80 = 0
simplify, divide by 10
89a - b + 8 = 0
b = 89a + 8
The only value for a that would give a single digit value for b would be 0
therefore
a = 0
b = 8
Original number 1089
1089 * 9 = 9801 the reverse
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