To identify the equation that represents Alexandra's variable expenses for last month, let's start by understanding the relationship between total expenses, fixed expenses, and variable expenses.
Total expenses are the sum of fixed expenses and variable expenses. Mathematically, this can be expressed as:
[tex]\[ \text{Total expenses} = \text{Fixed expenses} + \text{Variable expenses} \][/tex]
From this, we can derive the equation to calculate variable expenses:
[tex]\[ \text{Variable expenses} = \text{Total expenses} - \text{Fixed expenses} \][/tex]
Given the values:
- Fixed expenses: \[tex]$1,832.76
- Total expenses: \$[/tex]4,295.82
We need an equation that shows the subtraction of fixed expenses from total expenses to determine the variable expenses. This model represents:
[tex]\[ v = \$4,295.82 - \$1,832.76 \][/tex]
By analyzing the provided options:
A. [tex]\( v = \$4,295.82 - \$1,832.76 \)[/tex]
B. [tex]\( v = \$1,832.76 - \$4,295.82 \)[/tex]
C. [tex]\( v = \$1,832.76 + \$4,295.82 \)[/tex]
D. [tex]\( v = \$2,463.06 + \$1,832.76 \)[/tex]
E. [tex]\( v = \$4,295.82 - \$2,463.06 \)[/tex]
Breaking down each option:
- Option A correctly represents the equation for calculating variable expenses by subtracting fixed expenses from total expenses.
- Option B subtracts total expenses from fixed expenses, which does not correctly represent the situation.
- Option C adds fixed expenses to total expenses, which is not the correct relationship.
- Option D adds a value derived from calculating variable expenses to fixed expenses, which also does not fit the correct equation.
- Option E uses a value calculated as variable expenses subtracted from total expenses but lists the wrong order.
Thus, the correct equation that represents Alexandria's variable expenses for last month is:
Option A: [tex]\( v = \$4,295.82 - \$1,832.76 \)[/tex]
