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

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Question 337815: George is thinking of a number between 70 and 90. The sum of the digits is less than 12. The product of the digits is greater than 25. What is George's number?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Let the ten's digit be t and the units digit be u

system%28t%2Bu%3C12%2Ctu%3E25%29

Since the number is between 70 and 90, t = 7 or t = 8

If t = 7 then

system%287%2Bu%3C12%2C7u%3E25%29

or

system%28u%3C5%2Cu%3E3%264%2F7%29

or u=4, the only digit that's greater than 3%264%2F7 and less than 5.

So one solution is 74.

We will see if there is another solution:

If t = 8 then

system%288%2Bu%3C12%2C8u%3E25%29

or

system%28u%3C4%2Cu%3E3%261%2F8%29

There is no digit greater than 3%261%2F8 and less than 4.

So 74 is the only solution.

Checking: 7+4=11 which is less that 12.
          7×4=28 which is greater than 25.
Edwin