SOLUTION: 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?

Question 66333This question is from textbook An Incremental Development
: 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? This question is from textbook An Incremental Development

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
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

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