Answer :
To determine which budget option will allow Alejandro to save at least [tex]$6000 for a car within the next two years, we need to evaluate each budget based on his income and expenses.
### Step-by-Step Solution:
1. Calculate Monthly Income:
- Alejandro makes $[/tex]10 per hour.
- He works 30 hours per week.
- Monthly income: [tex]\( \$10 \times 30 \text{ hours/week} \times 4 \text{ weeks/month} = \$1200 \)[/tex].
- According to the table, it appears there are two options for income: [tex]$1500 and $[/tex]1200, possibly indicating different hours worked or additional income sources.
2. Calculate Monthly Expenses for Each Budget:
- Let's break down and sum up the expenses for each budget:
- Budget A:
- Rent: [tex]$600 - Utilities: $[/tex]100
- Food: [tex]$150 - Bus Pass: $[/tex]250
- Savings: [tex]$25 - Total Expenses: \( \$[/tex]600 + \[tex]$100 + \$[/tex]150 + \[tex]$250 + \$[/tex]25 = \[tex]$1125 \) - Budget B: - Rent: $[/tex]600
- Utilities: [tex]$100 - Food: $[/tex]550
- Bus Pass: [tex]$250 - Savings: $[/tex]25
- Total Expenses: [tex]\( \$600 + \$100 + \$550 + \$250 + \$25 = \$1525 \)[/tex]
- Budget C:
- Rent: [tex]$600 - Utilities: $[/tex]100
- Food: [tex]$250 - Bus Pass: $[/tex]250
- Savings: [tex]$25 - Total Expenses: \( \$[/tex]600 + \[tex]$100 + \$[/tex]250 + \[tex]$250 + \$[/tex]25 = \[tex]$1225 \) - Budget D: - Rent: $[/tex]600
- Utilities: [tex]$100 - Food: $[/tex]150
- Bus Pass: [tex]$250 - Savings: $[/tex]25
- Total Expenses: [tex]\( \$600 + \$100 + \$150 + \$250 + \$25 = \$1125 \)[/tex]
3. Calculate Leftover Money for Each Budget:
- Budget A:
- Income: [tex]$1500 - Expenses: $[/tex]1125
- Leftover: [tex]\( \$1500 - \$1125 = \$375 \)[/tex]
- Budget B:
- Income: [tex]$1500 - Expenses: $[/tex]1525
- Leftover: [tex]\( \$1500 - \$1525 = -\$25 \)[/tex]
- Alejandro would have a deficit of [tex]$25 monthly. - Budget C: - Income: $[/tex]1200
- Expenses: [tex]$1225 - Leftover: \( \$[/tex]1200 - \[tex]$1225 = -\$[/tex]25 \)
- Alejandro would have a deficit of [tex]$25 monthly. - Budget D: - Income: $[/tex]1200
- Expenses: [tex]$1125 - Leftover: \( \$[/tex]1200 - \[tex]$1125 = \$[/tex]75 \)
4. Calculate Total Savings Over 2 Years (24 months):
- Budget A:
- Monthly leftover savings: [tex]$375 - Total savings after 24 months: \( \$[/tex]375 \times 24 = \[tex]$9000 \) - Budget B: - Monthly leftover savings: -$[/tex]25
- Total savings after 24 months: [tex]\( -\$25 \times 24 = -\$600 \)[/tex]
- Alejandro cannot save any money and will accumulate debt.
- Budget C:
- Monthly leftover savings: -[tex]$25 - Total savings after 24 months: \( -\$[/tex]25 \times 24 = -\[tex]$600 \) - Alejandro cannot save any money and will accumulate debt. - Budget D: - Monthly leftover savings: $[/tex]75
- Total savings after 24 months: [tex]\( \$75 \times 24 = \$1800 \)[/tex]
5. Evaluate Which Budget Allows Alejandro to Save [tex]$6000: - Among all the budgets, only Budget A allows Alejandro to save $[/tex]6000 within 2 years. In fact, under Budget A, he can save [tex]$9000 in 2 years. - Budgets B and C result in debt scenarios. - Budget D only allows saving $[/tex]1800 in 2 years, which is insufficient for Alejandro's goal.
### Conclusion:
The best option for Alejandro to save at least $6000 for a car within the next 2 years is:
a. Budget A
- He works 30 hours per week.
- Monthly income: [tex]\( \$10 \times 30 \text{ hours/week} \times 4 \text{ weeks/month} = \$1200 \)[/tex].
- According to the table, it appears there are two options for income: [tex]$1500 and $[/tex]1200, possibly indicating different hours worked or additional income sources.
2. Calculate Monthly Expenses for Each Budget:
- Let's break down and sum up the expenses for each budget:
- Budget A:
- Rent: [tex]$600 - Utilities: $[/tex]100
- Food: [tex]$150 - Bus Pass: $[/tex]250
- Savings: [tex]$25 - Total Expenses: \( \$[/tex]600 + \[tex]$100 + \$[/tex]150 + \[tex]$250 + \$[/tex]25 = \[tex]$1125 \) - Budget B: - Rent: $[/tex]600
- Utilities: [tex]$100 - Food: $[/tex]550
- Bus Pass: [tex]$250 - Savings: $[/tex]25
- Total Expenses: [tex]\( \$600 + \$100 + \$550 + \$250 + \$25 = \$1525 \)[/tex]
- Budget C:
- Rent: [tex]$600 - Utilities: $[/tex]100
- Food: [tex]$250 - Bus Pass: $[/tex]250
- Savings: [tex]$25 - Total Expenses: \( \$[/tex]600 + \[tex]$100 + \$[/tex]250 + \[tex]$250 + \$[/tex]25 = \[tex]$1225 \) - Budget D: - Rent: $[/tex]600
- Utilities: [tex]$100 - Food: $[/tex]150
- Bus Pass: [tex]$250 - Savings: $[/tex]25
- Total Expenses: [tex]\( \$600 + \$100 + \$150 + \$250 + \$25 = \$1125 \)[/tex]
3. Calculate Leftover Money for Each Budget:
- Budget A:
- Income: [tex]$1500 - Expenses: $[/tex]1125
- Leftover: [tex]\( \$1500 - \$1125 = \$375 \)[/tex]
- Budget B:
- Income: [tex]$1500 - Expenses: $[/tex]1525
- Leftover: [tex]\( \$1500 - \$1525 = -\$25 \)[/tex]
- Alejandro would have a deficit of [tex]$25 monthly. - Budget C: - Income: $[/tex]1200
- Expenses: [tex]$1225 - Leftover: \( \$[/tex]1200 - \[tex]$1225 = -\$[/tex]25 \)
- Alejandro would have a deficit of [tex]$25 monthly. - Budget D: - Income: $[/tex]1200
- Expenses: [tex]$1125 - Leftover: \( \$[/tex]1200 - \[tex]$1125 = \$[/tex]75 \)
4. Calculate Total Savings Over 2 Years (24 months):
- Budget A:
- Monthly leftover savings: [tex]$375 - Total savings after 24 months: \( \$[/tex]375 \times 24 = \[tex]$9000 \) - Budget B: - Monthly leftover savings: -$[/tex]25
- Total savings after 24 months: [tex]\( -\$25 \times 24 = -\$600 \)[/tex]
- Alejandro cannot save any money and will accumulate debt.
- Budget C:
- Monthly leftover savings: -[tex]$25 - Total savings after 24 months: \( -\$[/tex]25 \times 24 = -\[tex]$600 \) - Alejandro cannot save any money and will accumulate debt. - Budget D: - Monthly leftover savings: $[/tex]75
- Total savings after 24 months: [tex]\( \$75 \times 24 = \$1800 \)[/tex]
5. Evaluate Which Budget Allows Alejandro to Save [tex]$6000: - Among all the budgets, only Budget A allows Alejandro to save $[/tex]6000 within 2 years. In fact, under Budget A, he can save [tex]$9000 in 2 years. - Budgets B and C result in debt scenarios. - Budget D only allows saving $[/tex]1800 in 2 years, which is insufficient for Alejandro's goal.
### Conclusion:
The best option for Alejandro to save at least $6000 for a car within the next 2 years is:
a. Budget A
