The sum of the digits in a two-digit number is 7. The new number obtained when the digits are reversed is 27 less than the original number. Find the original number.

Question

diyadiya · Answer

Let the two digit number be xy 
Its given that the sum of the digits in a two-digit number is 7
So what do you think will be the first equation ?

anonymous · Answer

x + y = 7  I had that part.....I just go wrong from there. 

Does is go something like (10x + y) - (10y + x) ?

diyadiya · Answer

Yeah you are almost right 
But check the question again ,its given "The new number obtained when the digits are reversed is 27 less than the original number."

original number is 10x+y 
and number obtained after reversing is 10y+x 
Now what will be the second equation ?
**we are multiplying by 10 since the digit is in the ten's place

anonymous · Answer

So it would be like 10x + y (original) - 27 = 10y + x?

diyadiya · Answer

Right!! :D 
Now i think you can reduce the equation to a more simpler form? can you?

anonymous · Answer

Like this? 

10x + y - 27 = 10y + x -------> 9x-27=9y 

Could 9x - 27 become 9(x-3)? divide by 9 and y=x-3?

diyadiya · Answer

Exactly !!:D

anonymous · Answer

then plug it in to our first equation? or second.....

anonymous · Answer

It's 52!!! We did it!

diyadiya · Answer

Yay !!! Good!!! :D

anonymous · Answer

Can you help me with some others?

diyadiya · Answer

Sure :D