Expert: Chanda Walker - 2/3/2009

Question
i need help on this one problem. i can't find out the original number!
It is, The units digit of a two digit number is 4 less than 6 times the tens digit.  If the digits are reversed, the new number is 2 less than 3 times the original number. Find the original number.

Answer
a two digit number:

y*(10) + x

but x = 6y - 4

So that digit can also be written as

10y + 6y - 4
16y - 4

Now let's reverse the number

x*(10) + y

let's do that substitution again

x = 6y - 4
(6y - 4)* 10 + y
60y - 40 + y
61y - 40 is the reversed number

we know

3(16y - 4) - 2 = 61y - 40

48y - 12 - 2 = 61y - 40
40 - 14 = 61y - 48y
26 = 13y
y = 2

Now, let's check all that!

The original number must have been
16y - 4
32 - 4
28

Is 8  the same as 4 less than 6 times 2?  Yep it is!  Great that looks good.

Now, let's reverse the number.  82.

Is 82 the same as 2 less than 3 times 28?

28*3 = 84

Let's subtract off that 2 and we get 82.  Ok!  That all works.

The original number was 28.