Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Hanna shops for socks that cost [tex]$2.99 per pair and blouses that cost $[/tex]12.99 each. Let [tex]\( x \)[/tex] represent the number of pairs of socks purchased, and [tex]\( y \)[/tex] represent the number of blouses purchased.

Which equation models the purchases she made with $43.92?

A. [tex]\( x + y = 15.98 \)[/tex]
B. [tex]\( x + y = 43.92 \)[/tex]
C. [tex]\( 43.92 x - 2.99 y = 12.99 \)[/tex]
D. [tex]\( 2.99 x + 12.99 y = 43.92 \)[/tex]


Sagot :

To determine the correct equation that models the purchases Hanna made, we need to set up the equation based on the costs of the items and the total amount spent.

1. Identify Variables and Costs:
- Let [tex]\( x \)[/tex] represent the number of pairs of socks purchased.
- Let [tex]\( y \)[/tex] represent the number of blouses purchased.
- The cost per pair of socks is \[tex]$2.99. - The cost per blouse is \$[/tex]12.99.

2. Formulate the Equation:
- The cost of [tex]\( x \)[/tex] pairs of socks would be [tex]\( 2.99x \)[/tex].
- The cost of [tex]\( y \)[/tex] blouses would be [tex]\( 12.99y \)[/tex].
- The total amount spent is \$43.92.

Putting this information together, the equation that models Hanna's purchases can be written as:
[tex]\[ 2.99x + 12.99y = 43.92 \][/tex]

Now, let's evaluate the given options to see which one matches our formulated equation:

1. [tex]\( x + y = 15.98 \)[/tex]
- This equation does not account for the individual costs of the socks and blouses. It simply sums the variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex], which is incorrect.

2. [tex]\( x + y = 43.92 \)[/tex]
- This equation incorrectly suggests that the simple sum of the number of socks and blouses equals the total amount spent, which is not correct.

3. [tex]\( 43.92x - 2.99y = 12.99 \)[/tex]
- This equation incorrectly uses the total amount and the costs with incorrect signs and placements. It does not model the total cost based on the purchases correctly.

4. [tex]\( 2.99x + 12.99y = 43.92 \)[/tex]
- This equation correctly sums up the individual costs of the socks and blouses to equal the total amount spent.

Therefore, the correct equation that models the purchases Hanna made is:
[tex]\[ 2.99x + 12.99y = 43.92 \][/tex]

This is the appropriate representation based on the given costs and total expenditure.
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.