SOLUTION: The sum of the digits is 9. If the digits are reversed, the new number is 45 more than the original number. Find the two digit number.

Question 26725: The sum of the digits is 9. If the digits are reversed, the new number is 45 more than the original number. Find the two digit number.
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
we could probably do this by looking:

Easy possibles are
18 and 81
27 and 72
36 and 63
45 and 54

Looking, 27+45 is 72 so 27 is your answer.

OK, mathematically...

Let tens be x and units be y --> x+y = 9
Also, (10y+x) - (10x+y) = 45
10y+x-10x-y = 45
9y-9x = 45

we have
y+x = 9
9y-9x = 45

multiply first by 9 and we get
9y+9x = 81
9y-9x = 45

Now subtract, leaving 18x = 36. So x = 2. Therefore, from x+y=9, y must be 7.

jon.

RELATED QUESTIONS
The sum of a two-digit number is 13. If the digits are reversed, the new number is 9 more (answered by edjones)

The sum of a two-digit number is 13. If the digits are reversed, the new number is 9 more (answered by shahfaisal221090)

The sum of e digits of a two digit number is 9. If the digits are reversed,the new number (answered by stanbon)

Use elimination to solve the problem. The sum of the digits of a two-digit number is... (answered by ankor@dixie-net.com,MathTherapy)

The sum of the digits of a two-digit number is 11. If the digits are reversed, the new... (answered by stanbon)

The sum of the digits of a two-digit number is 11. If the digits are reversed, the new... (answered by josmiceli)

A number is 9 more than the sum of the digits. If the digits are reversed, the new... (answered by mananth)

URGENT HELP: The sum of the digits of a two-digit number is 9. If the digits are... (answered by fcabanski)

The sum of the digits of a two-digit number is 13. If the digits are reversed, the... (answered by macston)