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John spent $24 of his savings on a watch and 1/5 of the remainder on a shirt. He still had 2/3 of his savings left. How much were his savings at first?

User Ronica
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1 Answer

1 vote
let's say he had "x" to start with.

how much is 1/5 of x? well is just (1/5)x or just x/5.

how much is 2/3 of x? well, is just (2/3)x or 2x/3.

we know those sum will add up to "x", let's check then.


\bf \stackrel{shirt}{\cfrac{x}{5}}+\stackrel{watch}{24}+\stackrel{leftover}{\cfrac{2x}{3}}=x\impliedby \begin{array}{llll} \textit{multiplying all by the \underline{LCD of 15}}\\\\ \textit{to get rid of the denominators} \end{array} \\\\\\ \boxed{15}\cdot \cfrac{x}{5}+\boxed{15}\cdot 24+\boxed{15}\cdot \cfrac{2x}{3}=\boxed{15}\cdot x\implies 3x+360+10x=15x \\\\\\ 13x+360=15x\implies 360=15x-13x\implies 360=2x \\\\\\ \cfrac{360}{2}=x \implies 180=x
User Hakob Sargsyan
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