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?
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
