SOLUTION: 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? I do understand systems of equations. And alth

Question 563056: 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?

I do understand systems of equations. And although it appears quite simple, I can't understand how my second equation should be set up. So far I have: x + y = 7
but I don't know how to mathematically express the term "reversing it's digits". FYI, the answer is 34.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
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?
============================
Let t = the tens digit
Let u = the units digit
Then t + u = 7 -> t = 7 - u
The number, n, can be represented as n = 10t + u = 10(7-u) + u = 70 - 9u
When the digits are reversed we have:
n + 9 = 10u + t = 10u + (7-u) = 9u + 7 -> n = 9u - 2
So we have two equations and two unknowns:
n = 70 - 9u
n = -2 + 9u
Adding the two equations gives
2n = 68
n = 34
So the number is 34

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