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Question 1636: The sum of two digits of a two digit number is seven. If the digits are reversed, the new number is nine less than the original number.
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Let t = tens digit
u = units digit
The value of the original number is ten times the tens digit plus the units digit. That is, 10 t + u.
If the digits are reversed, then u becomes the tens digit, and t becomes the units digit, and the value of the number is 10u + t.
Since there are two variables, you need to find two equations.
"The sum of the digits is seven."
t + u = 7
"If digits are reversed, the new number is nine less than the original."
10u + t = 10t + u - 9.
Simplify this equation by subtracting 10t and u from each side of the equation.
10u + t - 10t - u = -9
Simplify this equation and divide both sides of the resulting equation by 9:
-9t + 9u = -9
-t + u = -1
Now you have two equations that you can add together:
t + u = 7
-t + u = -1
2u = 6
u = 3
Since the sum of the digits is 7, that makes t = 4.
The original number is 43, and the new number, with digits reversed, is 34.
Check: When the digits are reversed, the new number is indeed 9 less than the original number.
R^2 at SCC
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