SOLUTION: I have two secret numbers. Each has two digits. The secret numbers have the same digits, only reversed. The difference between the two numbers is 54, and the sum of the digits in e

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Question 170825: I have two secret numbers. Each has two digits. The secret numbers have the same digits, only reversed. The difference between the two numbers is 54, and the sum of the digits in each number is 10. What are my two secret numbers?
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!

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%28b=2%29 one digit
9a-9(2)=54 --->9a=72
:
highlight%28a=8%292nd digit
secret numbers aresystem%2828%2C82%29