SOLUTION: The sum of the digits of a two-digit number is 7. When the digits are reversed, the number formed is 27 more than the original number. Find the original number.
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Question 158853: The sum of the digits of a two-digit number is 7. When the digits are reversed, the number formed is 27 more than the original number. Find the original number.
You can put this solution on YOUR website! The sum of the digits of a two-digit number is 7. When the digits are reversed, the number formed is 27 more than the original number. Find the original number.
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Let x = ones digit
and y = tens digit
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from: "The sum of the digits of a two-digit number is 7."
x+y =7 (equation 1)
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from: "When the digits are reversed, the number formed is 27 more than the original number."
10x + y = (10y + x) + 27
9x = 9y + 27
x = y + 3 (equation 2)
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Solve equation 1 for y:
x+y =7
y =7-x
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Substitute the above into equation 2 and solve for x:
x = y + 3
x = 7-x + 3
2x = 7+3
2x = 10
x = 5 (ones digit)
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Subsitute the above into equation 1 and solve for y:
x+y =7
5+y =7
y = 7-5
y = 2
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Solution: The original number is 27
