Let's analyze the costs associated with each of the three options Joshua has:
1. Rent a computer for three weeks and get his old computer fixed:
- The rental price per week is \[tex]$30.
- Joshua needs to rent the computer for 3 weeks.
- The repair cost for his old computer is \$[/tex]75.
First, calculate the total rental cost for 3 weeks:
[tex]\[
\text{Total rental cost} = \$30 \text{ per week} \times 3 \text{ weeks} = \$90
\][/tex]
Next, add the repair cost:
[tex]\[
\text{Total cost for renting and repair} = \$90 + \$75 = \$165
\][/tex]
2. Pay cash for a new computer:
- The retail price of a new computer is \[tex]$1,000.
\[
\text{Total cost for buying a new computer} = \$[/tex]1,000
\]
3. Use an installment plan to buy a new computer:
- The installment plan requires \[tex]$100 per month for 12 months.
\[
\text{Total installment cost} = \$[/tex]100 \text{ per month} \times 12 \text{ months} = \[tex]$1,200
\]
Now, let's summarize the total costs for each option:
- Renting and repairing: \$[/tex]165
- Paying cash for a new computer: \[tex]$1,000
- Installment plan: \$[/tex]1,200
To determine the least expensive option, we compare the total costs:
[tex]\[
\min(\$165, \$1,000, \$1,200) = \$165
\][/tex]
Therefore, the least expensive option for Joshua is to rent a computer for three weeks and get his old computer fixed, costing him a total of \$165.
