SOLUTION: The sum of the digits of a two digit number is 9. If the digits are reversed, the number formed bears the ratio 3:8 to the original number. Find the original number (Ans. 77)

Question 567574: The sum of the digits of a two digit number is 9. If the digits are reversed, the number formed bears the ratio 3:8 to the original number. Find the original number (Ans. 77)
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
let the tens digit =
Let the units digit =
The actual number is
The number with the digits reversed is
given:
(1)
(2)
------------
Multiply both sides of (2) by
(2)
(2)
(2)
(2)
(2)
(2)
Substitute (2) into (1)
(1)
(1)
(1)
(1)
and, since
(1)
(1)
(1)
The original number is 72
check answer:
(2)
(2)
(2)
Multiply both sides by
(2)
(2)
OK
Note that the answer is impossible,
since the digits have to add up to
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