Let's start by analyzing the cost details provided for each item and the payment methods available.
### Calculating Costs for the Television
Rent-to-Own Program:
- Payment: [tex]$65 per week
- Total number of weeks in a year: 52
So the yearly cost for the TV under the rent-to-own program is:
\[ 65 \text{ dollars/week} \times 52 \text{ weeks} = 3380 \text{ dollars} \]
Installment Plan:
- Payment: $[/tex]146 per month
- Total number of months in a year: 12
So the yearly cost for the TV under the installment plan is:
[tex]\[ 146 \text{ dollars/month} \times 12 \text{ months} = 1752 \text{ dollars} \][/tex]
Extra Amount Paid Using Rent-to-Own Program:
[tex]\[ \text{Rent-to-own yearly cost} - \text{Installment yearly cost} = 3380 \text{ dollars} - 1752 \text{ dollars} = 1628 \text{ dollars} \][/tex]
Hence, Maria will pay an extra [tex]$1628 if she uses the rent-to-own program to buy the television.
### Monthly Budget Analysis for Installment Plan
If Maria uses the installment plan, we also need to calculate her total monthly cost for the three items:
- TV: $[/tex]146 per month
- Computer: [tex]$100 per month
- Refrigerator: $[/tex]80 per month
Total monthly cost:
[tex]\[ 146 + 100 + 80 = 326 \text{ dollars/month} \][/tex]
Given that Maria's monthly budget is [tex]$200, we need to determine how many items she can afford with this budget. Since the largest single installment is for the refrigerator at $[/tex]80 per month, let's analyze:
[tex]\[ \text{Monthly budget} \div \text{Cost of refrigerator} = 200 \text{ dollars} \div 80 \text{ dollars} = 2.5 \][/tex]
Since Maria can afford only whole items, and looking at completions of installments, she can afford the payments for 2 items within her monthly budget of $200.
So, Maria will be able to afford 2 items if she uses the installment plan.
