Reversing Number!
Algebra
Level
2
The ten’s digit of a two-digit number is twice the unit’s digit. Reversing the digits yields a new number that is 27 less than the original number. So what was the original number?
63
35
25
17
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
Let t be the ten's digit and u be the unit's digit. The first sentence transformed into an equation is
t = 2 u (equation 1)
The original number is 1 0 t + u and the reverse number is 1 0 u + t .
From the second sentence, the equation is
1 0 u + t = 1 0 t + u − 2 7 (equation 2)
Substitute (equation 1) in (equation 2), then simplify
1 0 u + t = 1 0 t + u − 2 7
1 0 u + 2 u = 1 0 ( 2 u ) + u − 2 7
1 2 u = 2 0 u + u − 2 7
u = 3
It follows that t = 2 ( 3 ) = 6
So the original number is 6 3 .