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Sophie's favorite number is a two-digit number. If she reverses the digits, the result is 45 less than her favorite number. Also, one digit is one less than double the other digit. What is Sophie's favorite number?

 May 14, 2023
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a=tens digit,  b=ones digit

 

10*a + b ==10*b + a + 45...............(1)

a ==2*b - 1......................................(2), solve for a, b

 

a==11 and b==6 - this solution does not work since a is a 2-digit number.

Try: b=2*a - 1 which gives:

 

a=-4  and  b ==-9

[-4 * 10 - 9] == - 49 - which appears to be Sophie's favorite number.

 

Check: -49 - ( - 94) ==45 - difference between them

              [2 * - 4] == - 8 which is 1 greater than - 9 or - 9 is one less that double the other (2 * - 4) = -8

 May 14, 2023

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