SOLUTION: I need to represent the following as an equation: "The sum of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?" The answer i

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Question 267268: I need to represent the following as an equation: "The sum of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?" The answer is 34. But, how do you represent the first 1/2 of the problem in an equation? I came up with several ways to represent the part of the equation that is the second half of the problem. I do not know how to represent "the sum of a certain two-digit number"...
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Let t = tens digit and u = units digit

Any two digit number is of the form where 't' and 'u' are whole numbers. For example, the number 23 has a tens digit of 2 and a units digit of 3. So t=2 and u=3 which means that

Because "The sum of the digits of a certain two-digit number is 7", we know that . So this the first equation.

And since "Reversing its digits increases the number by 9", this tells us that . This is the second equation.

I'll let you solve the system of equations.

Answer by stanbon(75887) (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?" The answer is 34.
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Let the number be 10t+u
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Equations:
t + u = 7
10u + t - (10t+u) = 9
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Rearrange the 2nd equation:
9u - 9t = 9
9u + 9t = 63
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18u = 72
u = 4
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Since t + u = 7, t = 3
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Ans: The number is 34
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Cheers,
Stan H.