Question 170825


lets call one number ab....which makes the other number ba
:
a two digit number is composed of tens and ones units so these can also be written as 10(a)+1(b) and 10(b)+1(a).  We know the difference between the two is 54.
:
(10a+b)-(10b+a)=54...eq 1
:
10a-a+b-10b=54
:
{{{9a-9b=54}}}
:
we also know that a+b=10..eq 2...therefore a=10-b.....plug a's value into simplified eq 1
:
9(10-b)-9b=54---->90-9b-9b=54
:
-18b=--36
:
{{{highlight(b=2)}}} one digit
9a-9(2)=54 --->9a=72
:
{{{highlight(a=8)}}}2nd digit

secret numbers are{{{system(28,82)}}}