Question 66333
The sum of the digits of a two-digit number is 15. if the digits are reversed, the new number is only 9 more than the original number. What was the original number?

Letx=1st digit
And y= 2nd digit

Now we are told that x+y=15------------our first equation

But the first number is 10x+y

Now we are also told that if the digits are reversed the new number (10y+x) is 9 more that the first number (10x+y).  So:

10y+x=10x+y+9 collecting like terms, we have

9y=9x+9  divide by 9
y=x+1 or
x-y=-1------------our second equation


(1) x+y=15
(2) x-y=-1

Add (1) and (2)
2x=14
x=7 first digit  

substitute x=7 in (1)
7+y=15
y=15-7
y=8  second digit

So our first number was 78 and our second number was 87

ck

7+8=15
15=15
87 is 9 more than 78


Hope this helps -----ptaylor