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CAHSEE Math 6.3 Mathematical Reasoning 171 Views
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Description:
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?
Transcript
- 00:03
Here’s an unshmoopy question you’ll find on an exam somewhere in life…
- 00:07
A solution containing 30% alcohol is mixed with a solution of pure alcohol to obtain
- 00:12
20 milligrams of a solution that is 70% alcohol.
- 00:17
To determine the amount of pure alcohol that was added to the solution,
- 00:20
the equation 0.3 times 20 minus x… plus x… equals 0.7 times 20… could be used.
Full Transcript
- 00:29
If, instead, 30 total milligrams were required,
- 00:32
which of the following equations shows the correct changes to the above original question?
- 00:37
And here are the potential answers…
- 00:41
That’s a huge cartload of information.
- 00:43
Let’s use the given equation to try to make sense of all of it.
- 00:47
0.3 times 20 minus x… plus x… equals 0.7 times 20.
- 00:53
0.3 is multiplied by 20 minus x.
- 00:56
0.3 refers to the solution that’s 30% alcohol.
- 01:00
But what does 20 minus x mean?
- 01:02
Well, 20 must be the resulting amount of solution, and x is the amount of pure alcohol that is added.
- 01:09
The solution is made up of an unknown amount of 30% alcohol and x amount of 100% alcohol.
- 01:17
20 minus x refers to the amount of 30% alcohol that’s used in the solution…
- 01:21
…because x plus the amount of 30 percent alcohol used should add up to 20 milligrams.
- 01:27
x plus 20 minus x equals 20. The result, 0.7 times 20, is the ending percentage
- 01:34
of alcohol multiplied the amount of solution or 20 milligrams.
- 01:41
So, now that we know what the equation means…
- 01:44
…what will happen to the equation if we suddenly decided that we want
- 01:47
30 milligrams of a 70% solution? Well, the end result will be 30 milligrams
- 01:52
of 70% solution instead of 20 milligrams of that 70% solution.
- 01:56
The new sum is 0.7 times 30, which means we can eliminate option B, which does not change
- 02:03
the ending total. If we want to end with 30 milligrams of solution,
- 02:07
then we also have to put in 30 milligrams of pure and 30% alcohol.
- 02:13
If x still represents the amount of pure alcohol we put in,
- 02:16
then x plus a mystery amount of 30% alcohol equals 30.
- 02:21
x plus 30 minus x equals 30.
- 02:23
0.3 times 20 minus x is replaced with 0.3 times 30 minus x.
- 02:29
That eliminates options A and D from the list, and since we already eliminated B…
- 02:34
…our answer is C.
- 02:35
As in, “Confusing.”
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CAHSEE Math: Algebra and Functions Drill 5, Problem 3. Solve the equation.
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