<< Chapter < Page | Chapter >> Page > |
Find the unit rate: $423$ miles to $18$ gallons of gas.
23.5 mpg
Find the unit rate: $406$ miles to $14.5$ gallons of gas.
28 mpg
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.
A unit price is a unit rate that gives the price of one item.
The grocery store charges $\text{\$3.99}$ for a case of $24$ bottles of water. What is the unit price?
What are we asked to find? We are asked to find the unit price, which is the price per bottle.
Write as a rate. | $\frac{\mathrm{\$3.99}}{\text{24 bottles}}$ |
Divide to find the unit price. | $\frac{\mathrm{\$0.16625}}{\text{1 bottle}}$ |
Round the result to the nearest penny. | $\frac{\mathrm{\$0.17}}{\text{1 bottle}}$ |
The unit price is approximately $\text{\$0.17}$ per bottle. Each bottle costs about $\text{\$0.17}.$
Find the unit price. Round your answer to the nearest cent if necessary.
$\text{24-pack}$ of juice boxes for $\text{\$6.99}$
$0.29/box
Find the unit price. Round your answer to the nearest cent if necessary.
$\text{24-pack}$ of bottles of ice tea for $\text{\$12.72}$
$0.53/bottle
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.
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?
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. | $\frac{\text{\$0.234\u2026}}{\text{1 load}}$ | $\frac{\text{\$0.199\u2026}}{\text{1 load}}$ |
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.
Find each unit price and then determine the better buy. Round to the nearest cent if necessary.
Brand A Storage Bags, $\text{\$4.59}$ for $40$ count, or Brand B Storage Bags, $\text{\$3.99}$ for $30$ count
Brand A costs $0.12 per bag. Brand B costs $0.13 per bag. Brand A is the better buy.
Find each unit price and then determine the better buy. Round to the nearest cent if necessary.
Brand C Chicken Noodle Soup, $\text{\$1.89}$ for $26$ ounces, or Brand D Chicken Noodle Soup, $\text{\$0.95}$ for $10.75$ ounces
Brand C costs $0.07 per ounce. Brand D costs $0.09 per ounce. Brand C is the better buy.
Notice in [link] 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.
Have you noticed that the examples in this section used the comparison words ratio of, to, per, in, for, on , and from ? When you translate phrases that include these words, you should think either ratio or rate. If the units measure the same quantity (length, time, etc.), you have a ratio. If the units are different, you have a rate. In both cases, you write a fraction.
Notification Switch
Would you like to follow the 'Prealgebra' conversation and receive update notifications?