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Question 442283: The Sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! If the digit is ab, then from the first statement you know that a + b = 7.
For the second statement, remember that ab = 10a + b (like 23 = 10*2 + 3).
So 10b + a = 10a + b + 9.
Using the first equation, we know a = 7 - b. Substitute 7 - b for a in the last equation.
10b + (7 - b) = 10(7 - b) + b + 9
10b + 7 - b = 70 - 10b + b + 9
9b + 7 = 79 - 9b
18b = 72
b = 4
a = 7 - 4 = 3
The number is 34. You can test this number in the given statements to check.
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