Rahm used a payment plan to purchase wood for a home project. The wood he bought cost [tex] \$500 [/tex]. The clerk at the store offered him this payment plan instead.

\begin{tabular}{|c|c|}
\hline
Money Down & Cost per Month for 12 Months \\
\hline
[tex] \$50 [/tex] & [tex] \$55 [/tex] \\
\hline
\end{tabular}

What's the difference in cost between the cash price and the payment plan?

A. [tex] \$395 [/tex]
B. [tex] \[tex]$110 [/tex]
C. [tex] \$[/tex]160 [/tex]
D. [tex] \$210 [/tex]



Answer :

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: \[ \boxed{\$[/tex] 210}
\]