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.
