Question

a store sells two different - sized containers of a certain greek yogurt. the stores sales of this greek yogurt totaled 1,277.94 dollars last month. the equation $5.48x + 7.30y = 1,277.94$ represents this situation, where $x$ is the number of smaller containers sold and $y$ is the number of larger containers sold. according to the equation, which of the following represents the price, in dollars, of each smaller container?
○ 7.30
○ 5.48x
○ 5.48
○ 7.30y

Explanation:

Step1: Understand the equation structure

In a linear equation representing total cost (like \( \text{Total} = \text{Price per item} \times \text{Number of items} + \text{Price per other item} \times \text{Number of other items} \)), the coefficient of the variable representing the number of a type of item is the price per that item.
Here, the equation is \( 5.48x + 7.30y = 1277.94 \), where \( x \) is the number of smaller containers. So the term \( 5.48x \) represents the total revenue from smaller containers, meaning \( 5.48 \) is the price per smaller container (since \( \text{Total from smaller} = \text{Price per smaller} \times \text{Number of smaller} \), so \( \text{Price per smaller} = 5.48 \)).

Step2: Analyze the options

• Option "7.30": This is the coefficient of \( y \), so it's the price per larger container, not smaller. Eliminate.
• Option "5.48x": This is the total revenue from smaller containers, not the price per smaller. Eliminate.
• Option "5.48": As per Step1, this is the price per smaller container. Correct.
• Option "7.30y": This is the total revenue from larger containers, not related to smaller. Eliminate.

Answer:

5.48