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Teachers & SchoolsCAHSEE 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?

Algebra | Percents |

CAHSEE Math | Number Sense |

Language | English Language |

Number Sense | Percentages |

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.