ShmoopTube

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And here's another shmoop du jour.

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If x ounces of a 10% salt solution…

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…are added with 20 ounces of a 50% salt solution to create a combined 35% salt solution,

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what would be the value of x, or the amount of the 10% salt solution?

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And here are the potential answers…

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Basically, a highly diluted salt solution is being poured into a bucket with a more

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concentrated solution…

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…and the question wants to know how much we need of the highly diluted amount so that

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the end result is a 35% salt solution.

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So, said another way, x many ounces of the 10% diluted stuff is added to 20 ounces of

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the 50% stuff; we want the total to be a 35% stuff.

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The actual salt content of the 10% solution is 0.1x oz., while the salt content of the

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50% solution is 0.5 times 20… or 10 oz.

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These two amounts added together must equal the salt content in the combined solution.

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So the combined equation looks like this:

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0.1x plus 10 equals .35x plus .35 times 20.

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If we simplify, we get .1x plus 10 equals .35x plus 7… which simplifies to 3 = .25x

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Divide both sides by .25 and we get x equals 12.

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So answer A is our guy.

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