identify the percent of change as an increase or decrease. Then find the percent of change

Question 1 15 books to 21 books

Question 2 60 cars to 24 cars

Nerd123
Jan 30, 2018

#1**+1 **

Question 1:

This question definitely suggests a percent increase since the number of books increased. In other words, 15 plus some percent of 15 equals 21 books.

15 + some percent of 15 = 21

Let's let x = some percent because we do not know what that is.

15 + x of 15 = 21

"Of" in mathematics means multiplication.

15+15x=21

Now, solve for x:

\(15+15x=21\) | Now, isolate x in this equation. |

\(15x=6\) | Divide by 15 from both sides. |

\(x=\frac{6}{15}=\frac{2}{5}=0.4\) | Of course, we want to the percent increase, so we must convert 0.4, currently in decimal format, to a percent. To do that, just multiply by 100 and slap a percent sign behind the number. |

\(x=0.4\Rightarrow 40\%\) | This, of course, is the increase. |

Question 2:

The same concept can be used to calculate the percent decrease. I know that this problem involves that since the original amount is greater than the ending amount.

60 cars - some percent of 60 cars = 24 cars

Let's let x equal some percent.

60 cars - x of 60 cars = 24 cars

As aforementioned, "of" is a direct indicator of multiplication in mathematics.

60-60x=24

\(60-60x=24\) | |

\(-60x=-36\) | Divide by -60 on both sides. |

\(x=\frac{-36}{-60}=\frac{3}{5}=0.6\) | Of course, this needs to be a percentage. Let's convert the answer into one. |

\(x=0.6\Rightarrow 60\%\) | Remember that this is a decrease. |

Note: I realize that I could have used the formula \(\frac{y_2-y_1}{y_1}*100\) to get the percent changed, but I think that the following methods allow you to understand what is occurring; the formula, on the other hand, does not.

TheXSquaredFactor
Jan 30, 2018

#1**+1 **

Best Answer

Question 1:

This question definitely suggests a percent increase since the number of books increased. In other words, 15 plus some percent of 15 equals 21 books.

15 + some percent of 15 = 21

Let's let x = some percent because we do not know what that is.

15 + x of 15 = 21

"Of" in mathematics means multiplication.

15+15x=21

Now, solve for x:

\(15+15x=21\) | Now, isolate x in this equation. |

\(15x=6\) | Divide by 15 from both sides. |

\(x=\frac{6}{15}=\frac{2}{5}=0.4\) | Of course, we want to the percent increase, so we must convert 0.4, currently in decimal format, to a percent. To do that, just multiply by 100 and slap a percent sign behind the number. |

\(x=0.4\Rightarrow 40\%\) | This, of course, is the increase. |

Question 2:

The same concept can be used to calculate the percent decrease. I know that this problem involves that since the original amount is greater than the ending amount.

60 cars - some percent of 60 cars = 24 cars

Let's let x equal some percent.

60 cars - x of 60 cars = 24 cars

As aforementioned, "of" is a direct indicator of multiplication in mathematics.

60-60x=24

\(60-60x=24\) | |

\(-60x=-36\) | Divide by -60 on both sides. |

\(x=\frac{-36}{-60}=\frac{3}{5}=0.6\) | Of course, this needs to be a percentage. Let's convert the answer into one. |

\(x=0.6\Rightarrow 60\%\) | Remember that this is a decrease. |

Note: I realize that I could have used the formula \(\frac{y_2-y_1}{y_1}*100\) to get the percent changed, but I think that the following methods allow you to understand what is occurring; the formula, on the other hand, does not.

TheXSquaredFactor
Jan 30, 2018