To determine which equation represents Alexandra's variable expenses for last month, we need to understand the relationship between her fixed expenses, total expenses, and variable expenses.
Let's start by defining:
- Fixed Expenses: The regular, recurring costs that Alexandra pays every month. These are given as \[tex]$1,832.76.
- Total Expenses: The sum of all expenses Alexandra had last month, which is given as \$[/tex]4,295.82.
- Variable Expenses: The additional costs that vary each month, which we need to calculate.
We know that total expenses are the sum of fixed expenses and variable expenses. Therefore, we can express this relationship with the equation:
[tex]\[ \text{Total Expenses} = \text{Fixed Expenses} + \text{Variable Expenses} \][/tex]
Substituting the given values:
[tex]\[ 4,295.82 = 1,832.76 + \text{Variable Expenses} \][/tex]
To isolate and find the variable expenses, we need to subtract the fixed expenses from the total expenses:
[tex]\[ \text{Variable Expenses} = 4,295.82 - 1,832.76 \][/tex]
This corresponds to Option A:
[tex]\[ \text{Variable Expenses} = \$4,295.82 - \$1,832.76 \][/tex]
To verify, let's identify the possible answers for the remaining options:
- Option B ([tex]\(v = \$1,832.76 - \$4,295.82\)[/tex]): This would result in a negative number, which doesn't make sense for expenses.
- Option C ([tex]\(v = \$1,832.76 + \$4,295.82\)[/tex]): This adds the fixed and total expenses, giving an incorrect result.
- Option D ([tex]\(v = \$2,463.06 + \$1,832.76\)[/tex]): This again adds numbers unnecessarily.
- Option E ([tex]\(v = \$4,295.82 - \$2,463.06\)[/tex]): This subtracts an unrelated number from the total expenses.
Therefore, the equation representing Alexandra's variable expenses for last month is:
[tex]\[ \boxed{A: \quad v = 4,295.82 - 1,832.76} \][/tex]
