The sum of the digits of a two-digit number is 12. A new number is formed when the digits are reversed that is 12 less than twice the original number. Find the new number.

Can someone lead me in the right direction? I want to find it myself, I'm just not sure of how to do that..
Thanks! :)

Question

The sum of the digits of a two-digit number is 12. A new number is formed when the digits are reversed that is 12 less than twice the original number. Find the new number.

Can someone lead me in the right direction? I want to find it myself, I'm just not sure of how to do that..
Thanks! :)

btaylor · Answer

original number:
10x+y (x is tens digit, y is ones digit)
new number:
10y+x

btaylor · Answer

x+y=12
10y + x = 2(10x+y) - 12
it's a system.

anonymous · Answer

So I just use any two numbers I want? Like 3 & 9?

btaylor · Answer

no, simplify the second equation into:
10y+x = 20x+2y+12
then solve for x or y (I'll solve for y)
8y=19x+12
no, with the first equation, y = 12-x. So wherever you see a y, replace it with 12-x
8(12-x)=18x+12
so now you can solve for x

anonymous · Answer

When I solve for x, will that give me one of the numbers? & Thank you for helping :)

btaylor · Answer

it will give you the x value. then use y=12-x to solve for y.
you want to find the new number, so do 10y+x

anonymous · Answer

Oh okay. Thank you!!