Select the correct answer.

Alexandra keeps a record of her fixed and total expenses each month. Last month, she spent a little more than usual on variable expenses.

Fixed expenses: [tex]$\$[/tex] 1,832.76[tex]$
Total expenses: $[/tex]\[tex]$ 4,295.82$[/tex]

Which equation represents Alexandra's variable expenses for last month?

A. [tex]$\quad v=\$[/tex] 4,295.82-\[tex]$ 1,832.76$[/tex]
B. [tex]$\quad v=\$[/tex] 1,832.76-\[tex]$ 4,295.82$[/tex]
C. [tex]$v=\$[/tex] 1,832.76+\[tex]$ 4,295.82$[/tex]
D. [tex]$\quad v=\$[/tex] 2,463.06+\[tex]$ 1,832.76$[/tex]
E. [tex]$v=\$[/tex] 4,295.82-\[tex]$ 2,463.06$[/tex]



Answer :

To determine which equation represents Alexandria's variable expenses for last month, we need to follow these steps:

1. Identify her fixed expenses:
- Fixed expenses = \[tex]$1,832.76 2. Identify her total expenses: - Total expenses = \$[/tex]4,295.82

3. To find the variable expenses, we subtract the fixed expenses from the total expenses. This can be represented by the equation:
[tex]\[ v = \text{Total Expenses} - \text{Fixed Expenses} \][/tex]
Substituting the given amounts into the equation:
[tex]\[ v = 4,295.82 - 1,832.76 \][/tex]

Now, we compare this with the given 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]

Option A directly matches our derived equation and accurately represents the calculation of variable expenses by subtracting fixed expenses from total expenses:
[tex]\[ v = 4,295.82 - 1,832.76 \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{A.\quad v=\$ 4,295.82-\$ 1,832.76} \][/tex]