SOLUTION: George is thinking of an integer between 70 and 90. The sum of the digits is less then 12 and the product of the digits is greater then 25. What is George's integer?

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Question 208306: George is thinking of an integer between 70 and 90. The sum
of the digits is less then 12 and the product of the digits
is greater then 25. What is George's integer?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
George is thinking of an integer between 70 and 90. The sum
of the digits is less then 12 and the product of the digits
is greater then 25. What is George's integer? 

Let the ten's digit (first digit) = t
Let the one's digit (second digit) = u

system%28t+%2B+u+%3C+12%2Ctu%3E25%29

To be between 70 and 90, then t is either 7 or 8. 

If t=7 then we have:

system%287+%2B+u+%3C+12%2C7u%3E25%29

system%28u+%3C+5%2Cu%3E25%2F7=3%264%2F7%29

The only digit between 5 and 3%264%2F7 is 4

So one solution is t=7 and u=4, and the integer is 74.

If t=8 then we have:

system%288+%2B+u+%3C+12%2C8u%3E25%29

system%28u+%3C+4%2Cu%3E25%2F7=3%261%2F8%29

There is no digit between 4 and 3%261%2F8.

So 74 is the only solution.

Edwin