SOLUTION: A certain number is between 10 and 100. Its value is 8 times the sum of its digits and if it is reduced by 45, its digits are reversed. Find the integer.

Question 1111861: A certain number is between 10 and 100. Its value is 8 times the sum of its digits and if it is reduced by 45, its digits are reversed. Find the integer.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The difference between a 2-digit integer and the 2-digit integer with the digits reversed is 9d, where d is the difference between the two digits.

In this problem, the difference is 45, so the difference between the two digits is 5.

Since the number is reduced when the digits are reversed, the tens digit is larger than the units digit.

So the only possible answers are 61, 72, 83, and 94.

Then the problem says the integer is 8 times the sum of its digits; that means it is a multiple of 8.

The only integer in the list of possible answers that is divisible by 8 is 72; so the answer must be 72.

CHECK: 72 = 8(7+2); 72-27 = 45
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