SOLUTION: Plz answer it's for my holidays homework. The sum of the digits of a two digit number is 15. If 9 is added to the number the digits are interchange. Find the numbers.

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Question 1084820: Plz answer it's for my holidays homework.
The sum of the digits of a two digit number is 15. If 9 is added to the number the digits are interchange. Find the numbers.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The sum of the digits of a two digit number is 15. If 9 is added to the number the digits are interchange.
Suppose the digits are x and y, so the number is 10x+%2B+y
if the sum of the digits of a two digit number is 15, we have
x%2By=15....solve for x
x=15-y..........eq.1
If 9 is added to the number the digits are interchange:
10x+%2B+y%2B9=10y+%2B+x
10x+%2B+y%2B9-10y+-+x=0
9x+-9y+=-9
x+-y+=-1....solve for x
x++=y-1.........eq.2
from eq.1 and eq2 we have
15-y+=y-1
15%2B1+=y%2By
16+=2y
highlight%28y=8%29 -> x++=8-1->highlight%28x=7%29
so the number is 10x+%2B+y=10%2A7%2B8=highlight%2878%29
check: If 9 is added to the number the digits are interchange:
78%2B9=87 so, the digits are interchange