Question 504497: I need your help about the applications of System of Linear Equations. This is the problem:
The sum of the digits of a two digit number is 10. If the digits are reversed, the new number is 18 less than the original number. Find the original number.
-thank you.
I'm having a hard time finding the right equation to use so please help me. :)
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The sum of the digits of a two digit number is 10. If the digits are reversed, the new number is 18 less than the original number. Find the original number.
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Let x = the original number
Let m = the digit representing the tens place
Let n = the digit representing the ones place
Since the number x is obtained by multiplying m by 10 and adding n to it, we can write:
10m + n = x
If the digits are reversed the number is 18 less, so we have:
10n + m = x - 18
The sum of the digits is 10:
m + n = 10
So we have 3 equations in 3 unkowns. Solve using your favorite method, substitution, elimination, etc.
You will get the answers m = 6, n = 4
So the number is 64
Check:
6 + 4 = 10
64 - 18 = 46
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