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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 11, 2023
 #1
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+1

Let the number be 10x+y     where x and y are single digit numbers and x is not 0

 

10y+x=10x+y-45       and     x=2y-1   or     y=2x-1

 

10y+x=10x+y-45

9y-9x=-45

y-x=-5

y=x-5

 

now

 

x=2y-1        or        y=2x-1

x=2(x-5)-1        or        y=2x-1

x=2x-11       or        x-5=2x-1

-x=-11             or        -x=4

x=11              or           x=-4

x is a one digit number so x=-4

y=x-5

y=-9

 

-40-9

=-49

 

check

-40-9 = -90-4   + 45

rhs = -45-4=-49 = lhs    true.

-9=2*-4-1   true

 

This is the second time this has been answered in the last few days.

 May 12, 2023

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