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

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) (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
:

:
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
:
one digit
9a-9(2)=54 --->9a=72
:
2nd digit
secret numbers are
RELATED QUESTIONS
I have two secret numbers. Each has two digits. The secret numbers have the same digits,... (answered by stanbon)

what two numbers have the same two digits, but the order of the digits is different. The... (answered by ankor@dixie-net.com,checkley77)

I m thinking of two numbers which have the same two digits. The sum of there digits is 9... (answered by josgarithmetic)

Two 2-digit numbers have the same digits. their sum is 77 and their difference is 27.... (answered by edjones)

two different numbers use the same two digits . the sum of the digits is 7, and the... (answered by scott8148)

two different numbers use the same two digits. The sume of the digits is 7, and the... (answered by htmentor)

You have two numbers made up of the digits 9, 8, 7, 5, 3, where each digit is used only... (answered by checkley77)

two 2 digit #'s have the same digits. Their sum is 77 and their difference is 27. What... (answered by tommyt3rd)

There are two two-digit numbers that satisfy the following conditions: (1) Each number... (answered by LinnW)