Calculating Unit Price

Lesson 1: Unit Pricing - Calculating Unit Price

   Constructing Knowledge

Sometimes stores charge different amounts for a certain item depending on the quantity of the item purchased at one time. Buying one item may be an option. Buying in bulk may be another option. At first, you might think that buying one item would cost less than buying more than one of that item. However, sometimes it costs less per item if packages or bulk amounts are purchased.

Wise shoppers compare prices to see which is the best deal. Expressing prices as unit price is one way to do price comparisons. A unit price is an extension of a unit rate.

Unit Rate a rate in which the second term is one. (example: 64 beats/1 minute)

Unit price a unit rate that involves prices, usually the price of one unit or one item.

Since unit rates and unit prices can involve different units, units must always be present in answers.

Calculating Unit Price

\(\text{unit price}=\frac{\text{price}}{\text{number of items}}\)

   Multimedia

A video describing the calculation of unit price is provided.

EXAMPLE 1

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At a local grocery store, bagels can be purchased for 30 cents each. When 6 bagels are purchased, the cost is $1.50. What is the unit price of 6 bagels for $1.50? Which offer has the lower unit price.

Solution

A price of $1.50 for 6 bagels is not a unit price because the cost is for more than one item. To determine the unit price for 6 bagels, the mathematical operation is division.

\(\begin{align} \text{unit price}&=\frac{\text{price}}{\text{number of items}} \\ \\ &=\frac{\$1.50}{6\,\text{bagels}} \\ \\ &=\$0.25/\text{bagel} \\ \end{align}\)

The offer of 6 bagels for $1.50 has the better unit price, $0.25/bagel compared to $0.30/bagel.

Putting each price as a unit price means a price comparison can be made, and a decision can be reached about which price is cheaper. In this case, buying 6 bagels results in a lower cost per bagel.




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