Let's solve the given problem step-by-step.
### Step 1: Determine Extra Amount Paid for Laptop Using Rent-to-Own
First, we need to calculate how much extra a consumer would pay if they used the rent-to-own option instead of paying cash for the laptop computer.
- Rent-to-own cost for the laptop is [tex]\( \$150 \times 12 \text{ months} \)[/tex].
- Cash price for the laptop is \[tex]$1000.
To find the extra cost, we subtract the cash price from the rent-to-own cost:
\[ \text{Extra cost for laptop} = (\$[/tex]150 \times 12) - \[tex]$1000 \]
\[ \text{Extra cost for laptop} = \$[/tex]1800 - \[tex]$1000 = \$[/tex]800 \]
### Step 2: Determine the Cheapest Option Overall
We need to compare the total costs of all items (laptop and refrigerator combined) for the different payment methods: cash, installment, and rent-to-own.
1. Total cost if paying cash:
- Laptop: \[tex]$1000
- Refrigerator: \$[/tex]800
- Total: \[tex]$1000 + \$[/tex]800 = \[tex]$1800
2. Total cost if using the installment plan:
- Laptop: \( \$[/tex]100.83 \times 12 \text{ months} \)
- Refrigerator: [tex]\( \$80.67 \times 12 \text{ months} \)[/tex]
- Total: (\[tex]$100.83 \times 12) + (\$[/tex]80.67 \times 12)
- Total: \[tex]$1209.96 + \$[/tex]968.04 = \[tex]$2178
3. Total cost if using rent-to-own:
- Laptop: \( \$[/tex]150 \times 12 \text{ months} \)
- Refrigerator: [tex]\( \$140 \times 12 \text{ months} \)[/tex]
- Total: (\[tex]$150 \times 12) + (\$[/tex]140 \times 12)
- Total: \[tex]$1800 + \$[/tex]1680 = \[tex]$3480
Comparing these:
- Cash payment total: \$[/tex]1800
- Installment plan total: \[tex]$2178
- Rent-to-own total: \$[/tex]3480
The cheapest option is \[tex]$1800 (cash payment).
### Step 3: Determine the Most Expensive Option Overall
From the totals calculated, we see that the most expensive option is the rent-to-own method with a total of \$[/tex]3480.
### Final Answers
- If they used the rent-to-own program to buy the computer, a consumer would pay an extra [tex]\(\boxed{800}\)[/tex] dollars.
- For all of the items, using [tex]\(\boxed{cash}\)[/tex] is the cheapest option over the life of the contract.
- The most expensive overall option is to use [tex]\(\boxed{rent-to-own}\)[/tex] to purchase the items.
