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Question

# The research department of a company that manufactures children's fruit drinks is experimenting with a news flavor. A $17.5 \%$ fructose solution is needed, but only $10 \%$ and $20 \%$ solutions are available. How many gallons of the $10 \%$ fructose solution should be mixed with the $20 \%$ fructose solution to obtain 20 gallons of a $17.5 \%$ fructose solution?

Solution

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$\textbf{Givens:}$

Let The number of gallons of $10\%$ solution and $20\%$ solution be $x$ and $y$, respectively.

$10\%$ solution will be mixed with the $20\%$ solution to obtain $20$ gallons of a $17.5\%$ solution

$x+y=20\hspace{1cm}(1)$

and

$10\%x+20\%y=17.5\%(20)$

$0.1x+0.2y=3.5$

or (multiply by $10$)

$x+2y=35\hspace{1cm}(2)$

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