A unit price is the amount of money a person has to spend for one item (or one unit of measurement for one item). The dollars per ounce of a salad is an example of a unit price, because it represents how much money we have to pay for one unit (one ounce) of salad. You can usually see unit prices in the grocery store next to the price of each item.
To calculate unit price, you could use the following formula:
\[\textrm{unit price} = \frac{\textrm{cost of the item}}{\textrm{amount of the item}}\]
1.
Two boxes of the same type of cereal are available. One box costs
$3.99 and is 18.8 ounces of cereal. Another box costs $2.49 and is 10.8
ounces of cereal.
You eat a lot of the cereal, so you will be buying plenty of it in the future. You want to know whether the bigger box of cereal will save you money if you buy that every time you go to the store. You can calculate the unit price to find out which box is cheaper per ounce.
One box is $3.99 for 18.8 ounces of cereal.
\[\textrm{unit price} = \frac{\$3.99}{18.8 \textrm{ounces}} \approx \$0.21223 \textrm{ per ounce}\]
The other box is $2.49 for 10.8 ounces of cereal.
\[\textrm{unit price} = \frac{\$2.49}{10.8 \textrm{ounces}} \approx \$0.23056 \textrm{ per ounce}\]
It is cheaper to buy the larger box because it has a lower unit price. It’s usually the case that you save money if you buy in bulk, but it’s sometimes not true.
2.
A fast food restaurant has two options for buying chicken nuggets.
A person can buy 4 chicken nuggets for $1.89 or they can buy 10 chicken
nuggets for $4.99. Which option costs less money per chicken nugget?
4 chicken nuggets cost $1.89.
\[\textrm{unit price} = \frac{\$1.89}{4 \textrm{ chicken nuggets}} = \$0.4725 \textrm{ per chicken nugget}\]
10 chicken nuggets cos $4.99
\[\textrm{unit price} = \frac{\$4.99}{10 \textrm{ chicken nuggets}} = \$0.499 \textrm{ per chicken nugget}\]
The four chicken nuggets are cheaper per nugget than the 10 chicken nuggets. If a person wanted to buy 20 chicken nuggets, they should buy five of the four piece chicken nuggets instead of two of the 10 piece chicken nuggets.
1. An electrician does a lot of home construction work. They would like to buy supplies in bulk in order to save money. A wholesale electrical supply company offers a box of 48 outlets for $74.99, a box of 100 outlets for $129, or a box of 150 outlets for $200. Which box is cheaper per outlet?
2. Two cords of wood are selling for $450. Five cords of wood are selling for $1,000. Which item is the better buy? In other words, which item has the lowest unit price?
3. A farmer is considering purchasing two different nearby plots of land. They are both approximately the same in terms of soil quality and landscape. One plot of land is 530 acres and will cost $1,855,000. Another plot of land is 380 acres and will cost $1,387,000. Which plot costs less per acre?
4. One drink costs $2.29 per bottle. It has 44 mg of caffeine. Another drink comes in a bottle that has the same ounces of drink, but it costs $4.49. It has 72 mg of caffeine.
A person is choosing between the two drinks based on caffeine and cost. They don’t mind having to drink extra liquid in order to get the caffeine. Which drink costs less per mg of caffeine?
5. A family is looking to purchase a new home. It costs money to heat the home in the winter. The cost of the most recent winter is a part of the home sale documents so that buyers can be aware of the cost of operating the home.
One home is 2,000 square feet. It cost $3,500 to heat over the winter. Another home is 2,800 square feet. It cost $4,800 to heat over the winter.
Which home was more cost efficient to heat, according to these numbers? In other words, which home had the smallest cost per square foot for heating?
6. You’re looking to purchase holiday lights. Amazon says the unit price is $0.16 per foot when you buy 2 strands, or $0.36 cents per food when you buy four strands. You suspect something is wrong, so you make the calculation yourself.
They come in strands of 170 feet. You could purchase 2 strands for $21.98, or you could purchase 4 strands for $39.99.
1. If someone wanted to increase the unit price of their item, which quantity should they increase: The cost of the item, or the amount of the item?
2. If someone wanted to decrease the unit price of their item, which quantity should they increase: The cost of the item, or the amount of the item?
3. Consider the relationship between a seller and a buyer. Which of the two parties would want a high unit price?