SOLUTION: A number consists of two digits whose sum is five. When the digits are reversed, the number is increased by nine. Find the number.

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Question 32011This question is from textbook Beginning Algebra
: A number consists of two digits whose sum is five. When the digits are reversed, the number is increased by nine. Find the number. This question is from textbook Beginning Algebra

Answer by mbarugel(146) About Me  (Show Source):
You can put this solution on YOUR website!
Hello!
Let's call X to the first digit and Y to the second digit. The two digit number is then written as:
10X+%2B+Y
For example, if the digits are 3 and 7 (the number is 37), then the above expression yields:
10%2A3+%2B+7+=+37
We know that the sum of the digits is 5, so we get the equation:
X%2BY=5
We also know that when we reverse the number, it increases by 9. This implies that:
10Y%2BX+=+10X%2BY%2B9
9Y+-+9X+=+9
Y+-+X+=+1
We can isolate Y from this equation:
Y+=+1+%2B+X
And replace it in the previous one:
X%2B1%2BX+=+5
Now solve for X:
1%2B2X+=+5
X+=+2
Since the sum is 5, then Y must be 3. Therefore, the number is 23.

I hope this helps!
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