Let's analyze the details of the problem:
1. The cost of each pair of socks is \[tex]$2.99.
2. The cost of each blouse is \$[/tex]12.99.
3. Hanna spent a total of \[tex]$43.92.
4. Let \( x \) represent the number of pairs of socks purchased.
5. Let \( y \) represent the number of blouses purchased.
To form an equation that represents this situation, we need to express the total expenditure in terms of \( x \) and \( y \).
1. Each pair of socks costs \$[/tex]2.99, so the total cost for [tex]\( x \)[/tex] pairs of socks would be [tex]\( 2.99x \)[/tex].
2. Each blouse costs \[tex]$12.99, so the total cost for \( y \) blouses would be \( 12.99y \).
Adding these costs together gives the total amount spent:
\[ 2.99x + 12.99y \]
Since Hanna spent a total of \$[/tex]43.92, we can set the sum of these costs equal to \$43.92:
[tex]\[ 2.99x + 12.99y = 43.92 \][/tex]
Now, let's check the given options:
1. [tex]\( x + y = 15.98 \)[/tex] - This equation does not take into account the cost of the socks and blouses or the total amount spent. It simply adds the number of items, which is not correct in this context.
2. [tex]\( x + y = 43.92 \)[/tex] - Similarly, this equation incorrectly represents the sum of socks and blouses as the total cost, which is incorrect.
3. [tex]\( 43.92x - 2.99y = 12.99 \)[/tex] - This equation mixes the total spent with the individual costs in an incorrect way.
4. [tex]\( 2.99x + 12.99y = 43.92 \)[/tex] - This equation accurately represents the total expenditure based on the cost of socks and blouses.
Thus, the correct equation that models the purchases Hanna made is:
[tex]\[ 2.99x + 12.99y = 43.92 \][/tex]
