SOLUTION: the sum of the digits of a two digit number is 7. when the digits are reversed the new number is two more than twice the orginal number. what is the orginal number?

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Question 548858: the sum of the digits of a two digit number is 7. when the digits are reversed the new number is two more than twice the orginal number. what is the orginal number?
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
The two-digit number is: xy.
Keep in mind that does not mean x*y.
Also, the value of xy is 10*x +y.
.
The reversed number is: yx
Its value is 10*y + x.
.
x+y = 7
so
x = 7-y
.
10*y +x = 2*(10*x +y) +2
.
10y + x = 20x+ 2y + 2
.
Substitute for x
.
10y +7-y = 20(7-y) +2y +2
9y + 7 = 140 -20y +2y + 2
9y +7 = 142 -18y
27y = 142 -7 = 135
y = 5
x = 7-5 = 2
.
The original number is 25.
.
Check using the reversed number.
The reversed number is 52.
Does it equal twice the original number + 2?
2*25 + 2 = 52
Correct
.
Done.