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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. The sum of the digits in her favorite number is 11. What is Sophie's favorite number?

 Jun 27, 2020
 #1
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10 x  + y  = 45   +   10y   + x              and   x+y = 11    or y = 11-x     sub this into the first equation

 

10x + 11-x  = 45 + 10(11-x) + x     and solve for 'x'

9x + 11 = 45 +110-9x

18x = 144

x = 8     then y = 3          favorite number is   83        reversed = 38 which is  45 less than 83

 Jun 27, 2020
 #2
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This is AoPS homework.  Stop cheating on your homework.

 Jun 30, 2020
 #3
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im not i just want help on this my family cant help me and im on the verge of getting it wrong and failing

Creampuff  Jul 1, 2020

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