SOLUTION: The sum of the digits of a two-digit number is 9. If the number is doubled, then decreased by 36, the answer is the original number with the digits reversed. Find the number.

Question 229903: The sum of the digits of a two-digit number is 9. If the number is doubled, then decreased by 36, the answer is the original number with the digits reversed. Find the number.

Thanks for helping!!!
Found 2 solutions by ankor@dixie-net.com, solver91311:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let the two digit = 10x + y
:
Write an equation for each statement
;
"The sum of the digits of a two-digit number is 9."
x + y = 9
or
y = (9-x); use this for substitution
:
" If the number is doubled, then decreased by 36, the answer is the original number with the digits reversed."
2(10x+y) - 36 = 10y + x
:
20x = 2y - 36 = 10y + x
:
20x - x = 10y - 2y + 36
:
19x = 8y + 36
:
Find the number.
:
Replace y with (9-x) in the above equation, find x:
19x = 8(9-x) + 36
19x = 72 - 8x + 36
19x + 8x = 72 + 36
27x = 108
x =
x = 4:
I'll let you find y, check solution in the given statement

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let represent the 10s digit of the original number and let represent the 1s digit.

The sum of the digits is 9:

The value of the original number:

Double the original number:

Less 36:

The number with the digits reversed:

So:

Substituting:

Solve for and then solve for

John

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