A chemist needs to create a 25% citrus mixture by adding 20 mL of a 80% citrus solution to a 5% citrus solution. How much of each is needed?

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A chemist needs to create a 25% citrus mixture by adding 20 mL of a 80% citrus solution to a 5% citrus solution. How much of each is needed?

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Answer 1 · 2015-08-25T00:19:43

You would have to use 55 mL of 5 % citrus solution, and we would get 75 mL of 25 % citrus solution.

Explanation:

80 % citrus means $"80 mL citrus"/"100 mL solution"$

So in 20 mL of 80 % citrus:

$"Volume of citrus" = 20 color(red)(cancel(color(black)("mL soln"))) × "80 mL citrus"/(100 color(red)(cancel(color(black)("mL soln")))) = "16 mL citrus"$

In $x " mL"$ of 5 % citrus,

$"Volume of citrus" = x color(red)(cancel(color(black)("mL soln"))) × "5 mL citrus"/(100 color(red)(cancel(color(black)("mL soln")))) = x/20 " mL citrus"$

We add $x " mL"$ of 5 % citrus to $"20 mL"$ of 80 % citrus to get $20+x " mL"$ of 25 % citrus.

$"Total volume of citrus" = (16 + x/20) " mL"$

$"Total volume of solution" = (20+x) " mL"$ .

$(16+x/20)/(20+x) = 25/100$

$100(16+x/20)= 25(20+x)$

$1600+5x=500+25x$

$20x = 1600-500 =1100$

$x = 1100/20$

$x = 55$

We have to add 55 mL of 5 % citrus to 20 mL of 80 % citrus and get 75 mL of 25 % citrus.

Check:

$(16+55/20)/(20+55) = 25/100$

$((320 +55)/20)/75 = 25/100$

$375/1500 = 25/100$

$1/4=1/4$

It checks!

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A chemist needs to create a 25% citrus mixture by adding 20 mL of a 80% citrus solution to a 5% citrus solution. How much of each is needed?

1 Answer

Explanation:

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