SOLUTION: The sum of the digits of a two digit counting number is 10. If the digits are reversed, the new number is two less than three times the original number. What is the original number

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Question 306765: The sum of the digits of a two digit counting number is 10. If the digits are reversed, the new number is two less than three times the original number. What is the original number?
Answer by dabanfield(803) About Me  (Show Source):
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The sum of the digits of a two digit counting number is 10. If the digits are reversed, the new number is two less than three times the original number. What is the original number?
Let x be the tens digit and y the units digit.
The original number then is 10*x + y. The new number is 10*y + x.
We have then:
1.) x + y = 10 and
2.) 3*(10*x + y) - 2 = 10*y + x
From 1.) we have x = 10 - y. Substituting 10 - y for x in 2.) we have:
3*(10*(10-y) + y) - 2 = 10*y + (10 - y)
3*(100 - 10y + y) - 2 = 10*y + (10 - y)
3*(100 - 9*y) - 2 = 10*y + (10 - y)
300 - 27*y - 2 = 10*y + 10 - y
298 - 27*y = 9*y + 10
36*y = 288
y = 8
Substituting 8 for y in 1.) above we have:
x + y = 10
x + 8 = 10
x = 2
The original number then is 28.