Let's solve the problem step-by-step.
### 1) Extra Cost for Buying the Television using Rent-to-Own Program
Retail price of the television: \[tex]$480
Rent-to-own payments for the television: \$[/tex]27 per week for one year.
First, we calculate the total cost of owning the television through the rent-to-own program:
[tex]\[ \text{Total Rent-to-own Cost for TV} = 27 \text{ (dollars/week)} \times 52 \text{ (weeks)} = 1404 \text{ dollars} \][/tex]
Next, we find out the extra cost for using the rent-to-own program instead of paying the retail price:
[tex]\[ \text{Extra Cost for TV} = \text{Total Rent-to-own Cost for TV} - \text{Retail Price} \][/tex]
[tex]\[ \text{Extra Cost for TV} = 1404 - 480 = 924 \text{ dollars} \][/tex]
So, Maria will pay an extra [tex]\( \$924 \)[/tex] if she uses the rent-to-own program to buy the television, rather than waiting until she saves up enough money to pay cash for it.
### 2) Time Needed for Saving to Buy the Refrigerator in Cash
Retail price of the refrigerator: \[tex]$800
Maria's monthly budget: \$[/tex]200
To find the number of months Maria needs to save enough money to pay cash for the refrigerator, we divide the retail price by the monthly budget:
[tex]\[ \text{Months to Save for Fridge} = \left\lfloor \frac{800 \text{ dollars}}{200 \text{ dollars/month}} \right\rfloor = 4 \text{ months} \][/tex]
Since the remainder (800 mod 200 = 0) is zero, there is no need to add an extra month.
So, if Maria saves her money and pays cash, she can purchase a refrigerator in 4 months.
### Final Answer
1. Maria will pay an extra [tex]\( \$924 \)[/tex] if she uses the rent-to-own program to buy the television.
2. If she saves her money and pays cash, she can purchase a refrigerator in 4 months.
