## Finding Unit Price

Sometimes we buy common household items ‘in bulk’, where several items are packaged together and sold for one price. To compare the prices of different sized packages, we need to find the unit price. To find the unit price, divide the total price by the number of items. A **unit price** is a unit rate for one item.

### Definition: Unit price

A **unit price** is a unit rate that gives the price of one item.

## Example

The grocery store charges \(\text{\$3.99}\) for a case of \(24\) bottles of water. What is the unit price?

### Solution

What are we asked to find? We are asked to find the unit price, which is the price per bottle.

Write as a rate. | \(\frac{\$3.99}{\text{24 bottles}}\) |

Divide to find the unit price. | \(\frac{\$0.16625}{\text{1 bottle}}\) |

Round the result to the nearest penny. | \(\frac{\$0.17}{\text{1 bottle}}\) |

The unit price is approximately \(\text{\$0.17}\) per bottle. Each bottle costs about \(\text{\$0.17}.\)

Unit prices are very useful if you comparison shop. The *better buy* is the item with the lower unit price. Most grocery stores list the unit price of each item on the shelves.

## Example

Paul is shopping for laundry detergent. At the grocery store, the liquid detergent is priced at \(\text{\$14.99}\) for \(64\) loads of laundry and the same brand of powder detergent is priced at \(\text{\$15.99}\) for \(80\) loads.

Which is the better buy, the liquid or the powder detergent?

### Solution

To compare the prices, we first find the unit price for each type of detergent.

Liquid | Powder | |

Write as a rate. | \(\frac{\text{\$14.99}}{\text{64 loads}}\) | \(\frac{\text{\$15.99}}{\text{80 loads}}\) |

Find the unit price. | \(\frac{\text{\$0.234…}}{\text{1 load}}\) | \(\frac{\text{\$0.199…}}{\text{1 load}}\) |

Round to the nearest cent. | \(\begin{array}{c}\text{\$0.23/load}\hfill \\ \text{(23 cents per load.)}\hfill \end{array}\) | \(\begin{array}{c}\text{\$0.20/load}\hfill \\ \text{(20 cents per load)}\hfill \end{array}\) |

Now we compare the unit prices. The unit price of the liquid detergent is about \(\text{\$0.23}\) per load and the unit price of the powder detergent is about \(\text{\$0.20}\) per load. The powder is the better buy.

Notice in the example above that we rounded the unit price to the nearest cent. Sometimes we may need to carry the division to one more place to see the difference between the unit prices.