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Question 230771: The sum of the digits of a two-digit number is 13. If the digits are reversed, the
new number is 27 greater than the original number. What is the original two-digit
number?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 10x + y = the original two digit number
:
The sum of the digits of a two-digit number is 13.
x + y = 13
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If the digits are reversed, the new number is 27 greater than the original number.
10y + x = 10x + y + 27
10y - y = 10x - x + 27
9y = 9x + 27
Simplify, divide by 9
y = x + 3
rearrange to:
-x + y = 3
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What is the original two-digit number
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Use elimination here
-x + y = 3
x + y = 13
----------------addition eliminates x
2y = 16
y = 8
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Find x
x + 8 = 13
x = 5
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58 is the number
;
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Check solution in the statement
If the digits are reversed, the new number is 27 greater than the original number.
85 = 58 + 27
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