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Henry spent 1/6 of his money and an additional $10 on food. He then spent 1/2 of the remaining money and an additional $7 on books. Given that he was left with $13, how much money did Henry have at first?

 Nov 4, 2021
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Let x be the amount of money Henry had

at first then

he spent 1/6 of x and additional $10 on food

 

     spent on food :      \( {1 \over 6}x +10\)
   now remaining money is :   \(x- {1 \over 6}x-10\)
                                        =     \( {5 \over 6}x-10\)
    He spent 1/2 of remaining money and additional  

    $  on books

   spent on books : \({1\over 2}({5\over 6}x-10)+7={5\over 12}x+2\)
  
   he was at the end left with $13

  =>        \(({5 \over 6}x-10)-({5 \over 12}x+2) = 13\)
   =>                 \( {5 \over 12}x-12=13\)
   =>          \({5 \over 12}x = 25 => x = 25 * {12 \over 5} = 60\)
 

so Henry had $60 at first

 Nov 7, 2021

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