In a number of two digits, the sum of the digits is 5. If the digits change their places, the new number so formed increases in value by 9. Find the number.

Help me solve this problem please.

Question

In a number of two digits, the sum of the digits is 5. If the digits change their places, the new number so formed increases in value by 9. Find the number.

Help me solve this problem please.

anonymous · Answer

2 and 3

anonymous · Answer

Let us call the digits O and T (for ones and tens).
O + T = 5
O*10+T = T*10+O+9

Solve for O and T.

mr.math · Answer

Let the number be xy, then:
$x+y=5$
$10x+y=10y+x-9$.

mr.math · Answer

Solve the system for x and y.

mr.math · Answer

x=2, y=2. So the number is 23.

anonymous · Answer

Whilst all that's correct... this is at a pretty basic level ;) I think simultaneous equations are a bit of overkill. 5 doesn't have many factors, assuming we're talking in integers.

23: 2+3 = 5.
32: 23+9.

anonymous · Answer

Well, but showing how to setup the problem solution using equations is the real purpose of the question. Not necessarily how trivial the answer result is.

anonymous · Answer

True. And a most excellent answer it was.

anonymous · Answer

Thank you.