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Unit Price and Best Buys

This lesson explains how to calculate unit price and use it to compare products sold in different sizes or quantities. Students learn the unit price formula, practice dividing total price by quantity, and apply the skill to real shopping situations to identify the best buy between competing options.

What Is Unit Price?

Unit price tells you how much a single unit of an item costs, whether that unit is one ounce, one liter, one item, or one pound. It is one of the most useful tools for smart shopping because stores rarely sell products in the same size package. A big jug of juice and a small bottle of juice cannot be compared fairly just by looking at their total prices — you need to know the cost of each one per unit of the product.

The Unit Price Formula

To find the unit price of an item, divide the total price by the total quantity:

$ u = \dfrac{p}{q} $

Here, $u$ is the unit price, $p$ is the total price, and $q$ is the quantity (the number of units, ounces, or liters in the package). The result tells you the price of just one unit, which makes it possible to compare two products directly even when their package sizes are different.

How to Find the Best Buy

Once you know the unit price of each option, the best buy is simply the option with the lowest unit price, not the lowest total price. A larger package almost always costs more overall, but it might still be the better deal if its unit price is lower. Follow these steps whenever you compare two or more products:

1. Make sure both quantities are measured in the same unit (ounces with ounces, or liters with liters).

2. Divide the total price by the quantity for each product to get its unit price.

3. Compare the unit prices and choose the smallest one as the best buy.

Worked Example: Comparing Cereal Boxes

Suppose a 16 ounce box of cereal costs $4.00$ dollars, and a 20 ounce box of the same cereal costs $4.60$ dollars. Which box is the better buy?

For the 16 ounce box: $ u = \dfrac{4.00}{16} = 0.25 $ dollars per ounce.

For the 20 ounce box: $ u = \dfrac{4.60}{20} = 0.23 $ dollars per ounce.

Since $0.23$ is less than $0.25$, the 20 ounce box is the better buy even though it has the higher total price.

Comparing two cereal box sizes by unit price rather than total price

Worked Example: Different Package Counts

Unit price comparisons also work when items come in packs instead of by weight. Suppose a 12-pack of water bottles costs $3.60$ dollars, and a 24-pack costs $6.72$ dollars. Which pack gives the lower price per bottle?

For the 12-pack: $ u = \dfrac{3.60}{12} = 0.30 $ dollars per bottle.

For the 24-pack: $ u = \dfrac{6.72}{24} = 0.28 $ dollars per bottle.

The 24-pack has a slightly lower unit price, so it is the better buy. Notice that once you convert both prices to a cost per bottle, comparing them becomes a simple matter of comparing two decimal numbers. This same strategy applies when a store offers a discount on one of the packages, which is covered in more detail in best buys with discount, where the sale price has to be worked out before the unit price comparison can be made.

Unit Price as a Rate

Because unit price is a constant rate, the relationship between total cost and quantity forms a straight line through the origin, and the unit price is the slope of that line. A steeper line means a higher unit price, while a flatter line means a lower unit price and therefore the better deal.

Brand A: cost grows at $0.25 per ounce, so the line has slope 0.25

Brand B: cost grows at $0.23 per ounce, a slightly flatter line and a better unit price

Comparing the two graphs, Brand B's line rises more slowly, confirming that it has the lower unit price and is the better buy for the same quantity purchased.

Why This Skill Matters

Unit price and best buy comparisons show up constantly outside the classroom, from grocery aisles to online shopping carts. Learning to divide price by quantity and compare fairly helps you make confident decisions whenever package sizes, discounts, or bundle deals make a simple price tag misleading on its own.

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Tx Grade 8