SOLUTION: The units digit of a two-digit is 5 more than the tens digit. If the digits are reversed and the new number is divided by the original the quotient is 2 and the remainder is 7. Wha

Question 1184835: The units digit of a two-digit is 5 more than the tens digit. If the digits are reversed and the new number is divided by the original the quotient is 2 and the remainder is 7. What is the original number?
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!

Clearly the problem is most easily solved by trial and error....

tens digit 1; the number is 16; 61/16 is not 2 remainder 7
tens digit 2; the number is 27; 72/27 is not 2 remainder 7
tens digit 3; the number is 38; 83/38 IS 2 remainder 7

ANSWER: 38

Algebraically....

Let the tens digit be x
Then the units digit is x+5

The original number is
The number with the digits reversed is

The new number divided by the original number gives quotient 2 and remainder 7:

The tens digit is x=3; the units digit is x+5=8

ANSWER: 38

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