Answer :
Let's start by summarizing the problem: Your actual wages for the month have been reduced by [tex]$200, so your new actual income is $[/tex]1050 instead of the budgeted [tex]$1250. To ensure your net income is positive, we need to adjust the expenses accordingly.
First, let's calculate the total budgeted expenses:
\[
\text{Total Budgeted Expenses} = 450 + 220 + 200 + 75 + 155 = 1100
\]
With an actual income of $[/tex]1050 and total budgeted expenses of [tex]$1100, the net income would be:
\[
\text{Actual Net Income} = 1050 - 1100 = -50
\]
Since the actual net income is negative (-$[/tex]50), we need to reduce the expenses to make the net income zero or positive. We proportionally reduce each expense by the same ratio to cover this deficit.
First, calculate the reduction ratio needed to cover the [tex]$50 deficit: \[ \text{Reduction Ratio} = \frac{\text{Deficit}}{\text{Total Expenses}} = \frac{50}{1100} \approx 0.04545 \] Now, reduce each category by this ratio: 1. Rent: \[ \text{Corrected Rent} = 450 - (450 \times 0.04545) \approx 429.55 \] 2. Utilities: \[ \text{Corrected Utilities} = 220 - (220 \times 0.04545) \approx 210.00 \] 3. Food: \[ \text{Corrected Food} = 200 - (200 \times 0.04545) \approx 190.91 \] 4. Clothes: \[ \text{Corrected Clothes} = 75 - (75 \times 0.04545) \approx 71.59 \] 5. Cell Phone: \[ \text{Corrected Cell Phone} = 155 - (155 \times 0.04545) \approx 147.95 \] Summarizing the new budget to ensure positive actual net income, we get: - Rent: Approximately $[/tex]429.55
- Utilities: Approximately [tex]$210.00 - Food: Approximately $[/tex]190.91
- Clothes: Approximately [tex]$71.59 - Cell Phone: Approximately $[/tex]147.95
Therefore, after the corrections, your new budget looks like this:
\begin{tabular}{|l|r|c|}
\hline Monthly Budget & \begin{tabular}{r}
Budgeted \\
Amount
\end{tabular} & Actual Amount \\
\hline Income & & \\
Wages & [tex]$\$[/tex] 1250[tex]$ & $[/tex]\[tex]$ 1050$[/tex] \\
\hline Expenses & & \\
Rent & [tex]$\$[/tex] 450[tex]$ & $[/tex]\[tex]$ 429.55$[/tex] \\
Utilities & [tex]$\$[/tex] 220[tex]$ & $[/tex]\[tex]$ 210.00$[/tex] \\
Food & [tex]$\$[/tex] 200[tex]$ & $[/tex]\[tex]$ 190.91$[/tex] \\
Clothes & [tex]$\$[/tex] 75[tex]$ & $[/tex]\[tex]$ 71.59$[/tex] \\
Cell Phone & [tex]$\$[/tex] 155[tex]$ & $[/tex]\[tex]$ 147.95$[/tex] \\
\hline Net Income & & [tex]$\$[/tex] 0$ \\
\hline
\end{tabular}
By making these adjustments to the expenses, the net income will be zero, thus making sure that there are no deficits.
First, calculate the reduction ratio needed to cover the [tex]$50 deficit: \[ \text{Reduction Ratio} = \frac{\text{Deficit}}{\text{Total Expenses}} = \frac{50}{1100} \approx 0.04545 \] Now, reduce each category by this ratio: 1. Rent: \[ \text{Corrected Rent} = 450 - (450 \times 0.04545) \approx 429.55 \] 2. Utilities: \[ \text{Corrected Utilities} = 220 - (220 \times 0.04545) \approx 210.00 \] 3. Food: \[ \text{Corrected Food} = 200 - (200 \times 0.04545) \approx 190.91 \] 4. Clothes: \[ \text{Corrected Clothes} = 75 - (75 \times 0.04545) \approx 71.59 \] 5. Cell Phone: \[ \text{Corrected Cell Phone} = 155 - (155 \times 0.04545) \approx 147.95 \] Summarizing the new budget to ensure positive actual net income, we get: - Rent: Approximately $[/tex]429.55
- Utilities: Approximately [tex]$210.00 - Food: Approximately $[/tex]190.91
- Clothes: Approximately [tex]$71.59 - Cell Phone: Approximately $[/tex]147.95
Therefore, after the corrections, your new budget looks like this:
\begin{tabular}{|l|r|c|}
\hline Monthly Budget & \begin{tabular}{r}
Budgeted \\
Amount
\end{tabular} & Actual Amount \\
\hline Income & & \\
Wages & [tex]$\$[/tex] 1250[tex]$ & $[/tex]\[tex]$ 1050$[/tex] \\
\hline Expenses & & \\
Rent & [tex]$\$[/tex] 450[tex]$ & $[/tex]\[tex]$ 429.55$[/tex] \\
Utilities & [tex]$\$[/tex] 220[tex]$ & $[/tex]\[tex]$ 210.00$[/tex] \\
Food & [tex]$\$[/tex] 200[tex]$ & $[/tex]\[tex]$ 190.91$[/tex] \\
Clothes & [tex]$\$[/tex] 75[tex]$ & $[/tex]\[tex]$ 71.59$[/tex] \\
Cell Phone & [tex]$\$[/tex] 155[tex]$ & $[/tex]\[tex]$ 147.95$[/tex] \\
\hline Net Income & & [tex]$\$[/tex] 0$ \\
\hline
\end{tabular}
By making these adjustments to the expenses, the net income will be zero, thus making sure that there are no deficits.
