ShmoopTube

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Time to get your shmoop on...

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Monty has 2.5 liters of a 4% solution and

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one container of 10% solution. How much 10% solution does he need to add

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to the 2.5 liters of the 4% solution to get a 6% solution?

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And here are the potential answers...

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Okay, It's all about concentration levels... like in a sports drink, really.

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Like... ever cut a bottle of Gatorade with water? Same idea.

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Let's say we just finished a brutal 2 on 1 against Kobe and Lebron and sweated 2.5 liters.

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The "watered down" Gatorade has 4% sugar; and the normal Gatorade has 10% sugar.

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We're sorta like the 3 bears in this sense -- we want the porridge neither too hot nor

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too cold...

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...the Gatorade has to be somewhere in between the 4 and the 10, and we think 6% is about

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the right concentration to replace the electrolytes we lost dragging Kobe and Lebron up and down the court.

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To help frame even further

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Now let's do the math. We can write 2.5 liters of 4% solution as

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2.5 times .04, which is 0.1.

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Monty has x liters of 10% solution, so x times .1 is .1x.

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Together, the 6% solution will have 2.5 liters plus x, which we can write as .06 times the

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quantity 2.5 plus x.

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Distributing the .06...we have .15 plus .06x. So if we set up the equation... 0.1 plus 0.1x

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equals .15 plus .06x. Combining like terms...which means grouping

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the x's together and the constants together, we get that .04x equals .05.

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Divide both sides by .04, and x equals 1.25, or 1 and 1/4 liters...

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Looks like B is our answer.

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