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CAHSEE Math Videos 210 videos

CAHSEE Math 1.1 Statistics, Data, and Probability I
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Statistics, Data, and Probability I: Drill Set 1, Problem 1. What is the mean yearly salary?

CAHSEE Math 1.2 Statistics, Data, and Probability I
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Statistics, Data, and Probability I: Drill Set 1, Problem 2. What is the median length of these writing utensils?

CAHSEE Math 1.3 Statistics, Data, and Probability I
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CAHSEE Math Statistics, Data, and Probability I: Drill Set 1, Problem 3. The mode of the number of days in each month for a single non-leap year is...

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CAHSEE Math 3.2 Number Sense 197 Views


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Description:

CAHSEE Math: Number Sense Drill 3, Problem 2. If a number is tripled and the result is halved, what is the percentage increase of the resulting number relative to the original?

Language:
English Language

Transcript

00:02

And here's your shmoop du jour...

00:04

If a number is tripled, and the result is halved...

00:06

...what is the percentage increase of the resulting number relative to the original?

00:11

Here are the potential answers...

00:15

Alright, well this is hard because,

00:16

they don't give us any specific numbers so we have to kinda... make stuff up.

00:22

So if x is the mysterious number they refer to,

00:25

X is tripled -- so we write it as 3x.

00:29

Next it's halved -- so we write it as 3x over 2.

00:33

The tricky part here is recognizing the NEW and OLD number in this problem...

00:38

...which is kind of a theoretical approach to the "new minus old over old" rate of

00:41

growth style problem.

00:43

We just plug in the new and the old...

00:45

...and we have 3x over 2 minus x... all over x

00:48

We have in the numerator 3x over 2 minus x over 1, which is the same as x.

00:54

Multiply top and bottom here by 2 and we have 2x over 2 so now we get x over 2;

00:59

Now divide it by x which is x over 1 And dividing by a fraction is the same as

01:03

multiplying by the reciprocal...

01:06

So we have x over 2x which is 1 half.

01:10

A quick scan of the answers and boom 50% is right there --

01:14

and the answer is A.

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