### 1.7 – Percents

# Percents

There are three types of percent problems.

What is 30% of 250? |
---|

This is the first type of percent problem. We will want to begin by writing it as a mathematical equation: Notice that we change the percentage to a decimal in order to use it in an equation. We will typically do this any time we use a percent mathematically. We can solve this equation simply enough by multiplying: |

25 is what percent of 400? |
---|

This is the second type of percent problem. Let’s rewrite it in a mathematical equation: Here, we can divide each side of the equation by 400: And then solve by performing the division: Notice here that when we solve for , we have a decimal. The question, however, asked for a percent, so we must convert this. We have |

8 is 12.5% of what number? |
---|

This is the third type of percent problem, translating into a mathematical equation gives: |

### Discount and Markup

Discounts and Markups are an application of percents:

A retail store sells t-shirts for $50. If they go on sale for 25% off, what is the discount, and what is the new sales price? |
---|

To find the discount amount, we simply need to find the value that is 25% of $50. That is, we need to solve the equation: Solving this equation simply involves multiplying the right hand side: So the discount is $12.50.To find the sale price then, we simply subtract the discount from the original price of the shirt. So the sales price is $37.50 |

A retail store purchases jeans at a price of $12 per pair. They then markup the price of the jeans by 40%. What is the markup, and the selling price of the jeans? |
---|

The markup is found by multiplying the markup percent by the purchase price: So the markup is $4.80The selling price of the jeans then is found by adding the markup to the purchase price. The jeans are sold for $16.80 |

### Percent Increase and Percent Decrease

**Percent increase** is the measure of an increase, as a percentage of the original value.

Percent Increase |
---|

Percent Increase can be found by the formula |

Jill pays rent of $400. Her landlord raises her rent to $420. What was her percent increase? |
---|

Jill’s new rent is $420, and her old rent was $400. Plugging these values into the formula yields: |

**Percent Decrease** is a measure of decrease, as a percent of the original amount.

Percent Decrease |
---|

Percent decrease is calculated very similarly to percent increase. It is, however, slightly different. The formula for percent decrease is: |

Trent usually purchases $320 worth of chicken feed every month. One month, he only purchases $240 worth. What was the percent decrease in his purchase? |
---|

Notice that for percent decrease, only the order of the difference in the numerator has changed. – We can substitute the values into this formula and simplify: |