SOLUTION: the sum of the digits of two digit number is 7. if the digits are interchanged, the resulting number is 27 more than the original number. find the original number.?

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Question 827154: the sum of the digits of two digit number is 7. if the digits are interchanged, the resulting number is 27 more than the original number. find the original number.?
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
all these are...are puzzles waiting to be solved
Sum and more than=adding
two digit number=## ex:(11, 35, 99, ...)
adding the digits together looks like: 1+1=2 for 11, 3+5=8 for 35, 9+9=18 for 99
these can also be viewed as variables for example say xy=35 where x=3 and y=5 but if 3 where to be multiplied by 5 you don't get 35. so what this really looks like is 3*10+5=35 highlight%2810x%2By%29=35 , and swapping positions is simply 35 to 53
with this in mind lets start the problem
we have numbers
xy where x%2By=7
yx where 10y%2Bx=27%2B10x%2By
now you have 2 equations so I'll solve for x first and substitute it in 2nd equation
x=7-y
10y%2B%287-y%29=27%2B10%287-y%29%2By
distribute the 10
10y%2B7-y=27%2B70-10y%2By
add like terms
9y%2B7=97-9y
add 9y to both sides and subtract 7 from both sides
18y=90
divide by 18
y=5
now simply solve for x by substituting in 5 for y
x=7-%285%29
x=2
the original number should behighlight_green%2825%29
Lets check
25%2B27=52
52=52
this is correct