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Sagot :
Alright, let's break down the steps to understanding the engineer's income, expenses, and balance based on the given information.
1. Calculate Monthly Net Pay:
The engineer earns a bi-weekly net pay of \[tex]$2,104.95. Since there are roughly two bi-weekly pay periods in a month, the monthly net pay can be calculated as: \[ \text{Monthly Net Pay} = 2 \times 2104.95 = 4209.90 \] 2. Calculate Monthly Expenses: The engineer allocates different percentages of the monthly net pay to various expense categories. Let's calculate the specific dollar amounts for each category: - Housing (30%): \[ \text{Housing} = 4209.90 \times 0.30 = 1262.97 \] - Food/Household (20%): \[ \text{Food/Household} = 4209.90 \times 0.20 = 841.98 \] - Savings (5%): \[ \text{Savings} = 4209.90 \times 0.05 = 210.495 \] - Transportation (10%): \[ \text{Transportation} = 4209.90 \times 0.10 = 420.99 \] - Debt (10%): \[ \text{Debt} = 4209.90 \times 0.10 = 420.99 \] - Entertainment (5%): \[ \text{Entertainment} = 4209.90 \times 0.05 = 210.495 \] - Medical/Personal Care (3%): \[ \text{Medical/Personal Care} = 4209.90 \times 0.03 = 126.297 \] - Giving (5%): \[ \text{Giving} = 4209.90 \times 0.05 = 210.495 \] - Clothing (2%): \[ \text{Clothing} = 4209.90 \times 0.02 = 84.198 \] - Miscellaneous (10%): \[ \text{Miscellaneous} = 4209.90 \times 0.10 = 420.99 \] 3. Sum of All Expenses: Let's add up all these expenses to find the total monthly expenses: \[ 1262.97 (\text{Housing}) + 841.98 (\text{Food/Household}) + 210.495 (\text{Savings}) + 420.99 (\text{Transportation}) + 420.99 (\text{Debt}) + 210.495 (\text{Entertainment}) + 126.297 (\text{Medical/Personal Care}) + 210.495 (\text{Giving}) + 84.198 (\text{Clothing}) + 420.99 (\text{Miscellaneous}) = 4209.90 \] 4. Calculate Balance: The balance is calculated by subtracting the total expenses from the monthly net pay: \[ \text{Balance} = 4209.90 (\text{Monthly Net Pay}) - 4209.90 (\text{Total Expenses}) = 9.09 \times 10^{-13} \] Given the result \(9.09 \times 10^{-13}\), the balance is practically equivalent to zero (it's a very small number due to floating-point arithmetic). Hence, the budget balances perfectly. Summary: The balance sheet for the engineer should look like this: - Monthly Net Pay: \$[/tex]4209.90
- Expenses:
- Housing: \[tex]$1262.97 - Food/Household: \$[/tex]841.98
- Savings: \[tex]$210.495 - Transportation: \$[/tex]420.99
- Debt: \[tex]$420.99 - Entertainment: \$[/tex]210.495
- Medical/Personal Care: \[tex]$126.297 - Giving: \$[/tex]210.495
- Clothing: \[tex]$84.198 - Miscellaneous: \$[/tex]420.99
- Total Expenses: \[tex]$4209.90 - Balance: \$[/tex]9.09 \times 10^{-13} (essentially zero)
This balance sheet correctly represents the engineer's income, expenses, and balance.
1. Calculate Monthly Net Pay:
The engineer earns a bi-weekly net pay of \[tex]$2,104.95. Since there are roughly two bi-weekly pay periods in a month, the monthly net pay can be calculated as: \[ \text{Monthly Net Pay} = 2 \times 2104.95 = 4209.90 \] 2. Calculate Monthly Expenses: The engineer allocates different percentages of the monthly net pay to various expense categories. Let's calculate the specific dollar amounts for each category: - Housing (30%): \[ \text{Housing} = 4209.90 \times 0.30 = 1262.97 \] - Food/Household (20%): \[ \text{Food/Household} = 4209.90 \times 0.20 = 841.98 \] - Savings (5%): \[ \text{Savings} = 4209.90 \times 0.05 = 210.495 \] - Transportation (10%): \[ \text{Transportation} = 4209.90 \times 0.10 = 420.99 \] - Debt (10%): \[ \text{Debt} = 4209.90 \times 0.10 = 420.99 \] - Entertainment (5%): \[ \text{Entertainment} = 4209.90 \times 0.05 = 210.495 \] - Medical/Personal Care (3%): \[ \text{Medical/Personal Care} = 4209.90 \times 0.03 = 126.297 \] - Giving (5%): \[ \text{Giving} = 4209.90 \times 0.05 = 210.495 \] - Clothing (2%): \[ \text{Clothing} = 4209.90 \times 0.02 = 84.198 \] - Miscellaneous (10%): \[ \text{Miscellaneous} = 4209.90 \times 0.10 = 420.99 \] 3. Sum of All Expenses: Let's add up all these expenses to find the total monthly expenses: \[ 1262.97 (\text{Housing}) + 841.98 (\text{Food/Household}) + 210.495 (\text{Savings}) + 420.99 (\text{Transportation}) + 420.99 (\text{Debt}) + 210.495 (\text{Entertainment}) + 126.297 (\text{Medical/Personal Care}) + 210.495 (\text{Giving}) + 84.198 (\text{Clothing}) + 420.99 (\text{Miscellaneous}) = 4209.90 \] 4. Calculate Balance: The balance is calculated by subtracting the total expenses from the monthly net pay: \[ \text{Balance} = 4209.90 (\text{Monthly Net Pay}) - 4209.90 (\text{Total Expenses}) = 9.09 \times 10^{-13} \] Given the result \(9.09 \times 10^{-13}\), the balance is practically equivalent to zero (it's a very small number due to floating-point arithmetic). Hence, the budget balances perfectly. Summary: The balance sheet for the engineer should look like this: - Monthly Net Pay: \$[/tex]4209.90
- Expenses:
- Housing: \[tex]$1262.97 - Food/Household: \$[/tex]841.98
- Savings: \[tex]$210.495 - Transportation: \$[/tex]420.99
- Debt: \[tex]$420.99 - Entertainment: \$[/tex]210.495
- Medical/Personal Care: \[tex]$126.297 - Giving: \$[/tex]210.495
- Clothing: \[tex]$84.198 - Miscellaneous: \$[/tex]420.99
- Total Expenses: \[tex]$4209.90 - Balance: \$[/tex]9.09 \times 10^{-13} (essentially zero)
This balance sheet correctly represents the engineer's income, expenses, and balance.
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