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?
|CAHSEE Math||Number Sense|
|Ratios, Percentages, and Proportions||Percent Change|
they don't give us any specific numbers so we have to kinda... make stuff up.
So if x is the mysterious number they refer to,
X is tripled -- so we write it as 3x.
Next it's halved -- so we write it as 3x over 2.
The tricky part here is recognizing the NEW and OLD number in this problem...
...which is kind of a theoretical approach to the "new minus old over old" rate of
growth style problem.
We just plug in the new and the old...
...and we have 3x over 2 minus x... all over x
We have in the numerator 3x over 2 minus x over 1, which is the same as x.
Multiply top and bottom here by 2 and we have 2x over 2 so now we get x over 2;
Now divide it by x which is x over 1 And dividing by a fraction is the same as
multiplying by the reciprocal...
So we have x over 2x which is 1 half.
A quick scan of the answers and boom 50% is right there --
and the answer is A.