# The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 9 less than three times the original number. What is the original number?

The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 9 less than three times the original number. What is the original number?
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Dakota Duarte
Let the unit digit be x and tens digit be y
then x+y=9 ........................(1)
and number is x+10y
On reversing the digits it will become 10x+y
As 10x+y is 9 less than three times x+10y, we have
10x+y=3(x+10y)−9
or 10x+y=3x+30y−9
or 7x−29y=−9 ........................(2)
Multiplying (1) by 29 and adding to (2), we get
$36x=9×29-9=9×28$
or $x=\frac{9×28}{36}=7$
and hence y=9−7=2
and number is 27.