SOLUTION: Jane selects a positive two digit integer. She multiplies the ones digit by five and the tens digit by three and adds the result. What was the original integer is her total is the

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Question 892614: Jane selects a positive two digit integer. She multiplies the ones digit by five and the tens digit by three and adds the result. What was the original integer is her total is the same as the integer she chose?
Answer by Edwin McCravy(20063)   (Show Source): You can put this solution on YOUR website!
tens digit = t
ones digit = u
number = 10t+u

the ones digit multiplied by five and the 
tens digit by three and the result added = 5u+3t

her total is the same as the integer she chose

   

Divide both sides by 4t

   

 

    

The only digits in the ratio u:t = 7:4 are u=7 and t=4.

So the number is 47.

Checking:  5×7+3×4 = 35+12 = 47

Edwin
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