Lesson 1: Unit Pricing - Unit Rates Extended

   Constructing Knowledge

Sometimes it is not practical to price items by a single unit. For example, in a grocery store, many items are priced per 100 grams because it is difficult to understand the size of one gram of beef or chicken. Similarly, breakfast cereal unit pricing is usually stated as a price per 100 g, rather than as a unit price per gram or as a price per piece of cereal.

EXAMPLE 1

In the bulk section at a grocery store, 100 grams of jelly beans cost $2.39. A 1 kilogram bag of the same jelly beans costs $24.49. What is the better deal?

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Solution


In this example, you can use proportional reasoning. You can express the 100 gram price as a price for 1 kilogram. Doing this involves using equivalent fractions.

Before using equivalent fractions, the units involved must be the same. You may remember from your previous math studies that 1 kilogram is equivalent to 1000 grams.

Set up equivalent fractions.



To get a denominator of 1000 g on the right side of the equation, the denominator on the left must be multiplied by 10. To maintain equivalency, the numerator on the left must also be multiplied by 10.



\[\begin{align} y&=\$2.39\times 10 \\ \\ &=\$23.90 \\ \end{align}\]
The bulk jelly beans cost $23.90/1000g. By unit price, purchasing the jelly beans from the bulk section is the better deal.

Alternate solution


You can also express the 1 kg price as a price per 100 grams. The process will be similar as in the first solution.

Set up equivalent fractions.



To get a denominator of 100 g on the right side of the equation, the denominator on the left must be divided by 10. To maintain equivalency, the numerator on the left must also be divided by 10.



\[\begin{align} p&=\frac{\$24.49}{10} \\ \\ &=\$2.45 \\ \end{align}\]
The one kilogram bag of jelly beans cost $2.45/100g. By unit price, purchasing the jelly beans from the bulk section is the better deal.


Now, it is your turn! Complete the questions in your Chapter 2, Lesson 1 Practice Makes Perfect that refer to Unit Rates Extended.



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