SOLUTION: There is a number, the 2nd digit of which is smaller than its 1st digit by 4. And if the number were divided by the digit's sum, the quotient would be 7. What might be the number?

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Question 476419: There is a number, the 2nd digit of which is smaller than its 1st digit by 4. And if the number were divided by the digit's sum, the quotient would be 7. What might be the number?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Let the first digit be t

the 2nd digit...is smaller than its 1st digit by 4.
Therefore the second digit is t-4.

The number is 10 times the first digit plus the second digit

The number = 10t + t-4 = 11t - 4

Digits' sum = t + t-4 = 2t - 4

if the number were divided by the digit's sum, the quotient would be 7
11t - 4
——————— = 7
 2t - 4 

Multiply both sides by (2t - 4)

11t - 4 = 7(2t - 4)

11t - 4 = 14t - 28

    -3t = -24

      t = 8

The second digit is t-4 = 8-4 = 4

So the number is 84.

Edwin