Certainly! Here's the step-by-step solution:
Rahm bought wood for a home project with a cash price of \[tex]$500. Instead of paying cash, he opted for a payment plan. The payment plan details are as follows:
- Money down: \$[/tex]50
- Monthly payment: \[tex]$55 for 12 months
First, let's calculate the total cost under the payment plan.
1. Calculate the total amount paid through the monthly installments:
\[
\text{Total monthly payments} = \text{Monthly payment} \times \text{Number of months} = 55 \times 12
\]
Simplifying this:
\[
55 \times 12 = 660
\]
2. Add the initial down payment to the total monthly payments to find the total cost of the payment plan:
\[
\text{Total cost of payment plan} = \text{Money down} + \text{Total monthly payments} = 50 + 660
\]
Simplifying this:
\[
50 + 660 = 710
\]
So, the total cost Rahm incurs with the payment plan is \$[/tex]710.
3. Determine the difference in cost between the payment plan and the cash price:
[tex]\[
\text{Difference in cost} = \text{Total cost of payment plan} - \text{Cash price} = 710 - 500
\][/tex]
Simplifying this:
[tex]\[
710 - 500 = 210
\][/tex]
Therefore, the difference in cost between the cash price and the payment plan is \[tex]$210.
So, the correct answer is:
\[
\boxed{\$[/tex] 210}
\]
