F1.5 Calculate unit rates for various goods and services, and identify which rates offer the best value.
Skill: Comparing Unit Rates
Students should be able to make price comparisons in order to determine the lowest price. By using mathematical ideas such as proportional reasoning, they can compare the price of a given quantity of the same product sold by different merchants. This mathematical skill will allow the student to limit the influence of the cognitive biases of marketing.
Here is an example of the sale of glue sticks in a retail store.
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Retail Store 1 |
Retail Store 2 |
Retail Store 3 |
|
|
Posted price |
$3 for 6 glue sticks |
$6 for 18 glue sticks |
$9 for 24 glue sticks |
The student should be able to compare the price, for an equal quantity, to determine the best purchase.
|
Retail Store 1 |
Retail Store 2 |
Retail Store 3 |
|
|
Posted price |
\(\div 6 \) $3 for 6 glue sticks |
\(\div 18 \) $6 for 18 glue sticks |
\(\div 24 \) $9 for 24 glue sticks |
|
Price calculated for 1 glue stick |
\(\div 6 \) \( \frac{$3}{6 \ \mathrm{sticks}} = \frac{$0.50}{1 \ \mathrm{stick}} \) |
\(\div 18 \) \( \frac{$6}{18 \ \mathrm{sticks}} = \frac{$0.33}{1 \ \mathrm{stick}} \) |
\(\div 24 \) \( \frac{$9}{24 \ \mathrm{sticks}} = \frac{$0.38}{1 \ \mathrm{stick}} \) |
With a unit price of $0.33/stick, the Retail Store 2 represents a cheaper option than the other two stores.
The student can also use the unit price by dividing the first term by the second term using a calculator if needed.
|
Retail Store 1 |
Retail Store 2 |
Retail Store 3 |
|
\( \frac{$3}{6 \ \mathrm{sticks}} = $0.50 / \mathrm{stick} \) |
\( \frac{$6}{18 \ \mathrm{sticks}} = $0.33 / \mathrm{stick} \) |
\( \frac{$9}{24 \ \mathrm{sticks}} = $0.38 / \mathrm{stick} \) |
Again, the price at Retail Store 2 is cheaper. The price for a glue stick, namely the unit price at Retail Store 2, is $0.33/stick.
Knowledge: Unit Cost (Cost per Unit)
The unit price represents the price or package per unit ($2.50 per apple, $15/hr, 15 m/s, etc.). This concept is often used when shopping at the grocery store. Many grocery stores will change the way they display prices, especially during promotions, to show a lower price. Instead of displaying the price per gram, some grocery stores will display the price per 100 g, or even per 50 g. Consumers should be sure to compare prices in order to take advantage of the most favourable packages.
This mathematical concept is not only used at the grocery store. Increasingly, companies are offering packages, for example, the cost of a cell phone package per month and depending on the number of lines associated with the account, the cost of an online television service per month, the cost for a number of gigabytes per month for Internet use. These companies offer different prices, and in most cases, the higher the quantity, the better the price per unit. However, it is important that the consumer not only considers the cost per unit, but also the total cost that can be paid in addition to the total amount of units needed.