SOLUTION: what two numbers have the same two digits, but the order of the digits is different. The sum of the digits is 8. The difference of the two numbers is 18. What are the two numbers?

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Question 344820: what two numbers have the same two digits, but the order of the digits is different. The sum of the digits is 8. The difference of the two numbers is 18. What are the two numbers?
Found 2 solutions by ankor@dixie-net.com, checkley77:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
what two numbers have the same two digits, but the order of the digits is different.
The sum of the digits is 8. The difference of the two numbers is 18. What are the two numbers?
:
Let x = original 10's digit
Let y = original units
then
10x + y = original two digit number
and
10y + x = the other number with the same digits
:
"The sum of the digits is 8."
x + y = 8
:
"The difference of the two numbers is 18."
(10x + y) - (10y + x) = 18
combine like terms
10x - x - 10y + y = 18
9x - 9y = 18
simplify, divide by 9
x - y = 2
x = (y + 2)
replace x in the 1st equation with (y+2)
(y+2) + y = 8
2y = 8 - 2
y =
y = 3
and
x = 3 + 2
x = 5
:
What are the two numbers? 53, 35

Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website!
10x+y-(10y+x)=18
x+y=8
x=8-y
10(8-y)+y-(10y+(8-y)=18
80-10y+y-10y-8+y=18
-18y=18-80+8
-18y=-54
y=3 ans.
x=8-3=5 ans.
Proof:
10*5+3-(10*3+5)=18
50+3-30-5=18
53-35=18
18=18