# CAHSEE Math 6.3 Mathematical Reasoning

CAHSEE Math Mathematical Reasoning Drill 6, Problem 3. If, instead, 30 total milligrams were required, which of the following equations shows the correct changes to the above original question?

 CAHSEE Math Mathematical Reasoning Language English Language Logic and Proofs Algebraic Proof

### Transcript

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If, instead, 30 total milligrams were required,

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which of the following equations shows the correct changes to the above original question?

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And here are the potential answers…

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That’s a huge cartload of information.

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Let’s use the given equation to try to make sense of all of it.

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0.3 times 20 minus x… plus x… equals 0.7 times 20.

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0.3 is multiplied by 20 minus x.

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0.3 refers to the solution that’s 30% alcohol.

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But what does 20 minus x mean?

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Well, 20 must be the resulting amount of solution, and x is the amount of pure alcohol that is added.

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The solution is made up of an unknown amount of 30% alcohol and x amount of 100% alcohol.

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20 minus x refers to the amount of 30% alcohol that’s used in the solution…

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…because x plus the amount of 30 percent alcohol used should add up to 20 milligrams.

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x plus 20 minus x equals 20. The result, 0.7 times 20, is the ending percentage

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of alcohol multiplied the amount of solution or 20 milligrams.

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So, now that we know what the equation means…

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…what will happen to the equation if we suddenly decided that we want

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30 milligrams of a 70% solution? Well, the end result will be 30 milligrams

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of 70% solution instead of 20 milligrams of that 70% solution.

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The new sum is 0.7 times 30, which means we can eliminate option B, which does not change

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the ending total. If we want to end with 30 milligrams of solution,

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then we also have to put in 30 milligrams of pure and 30% alcohol.

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If x still represents the amount of pure alcohol we put in,

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then x plus a mystery amount of 30% alcohol equals 30.

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x plus 30 minus x equals 30.

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0.3 times 20 minus x is replaced with 0.3 times 30 minus x.

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That eliminates options A and D from the list, and since we already eliminated B…

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