Let's break down the problem step-by-step.
1. Down Payment:
- Adam makes an 8% down payment on the total purchase price [tex]\( y \)[/tex].
- The down payment can be calculated as [tex]\( 0.08y \)[/tex].
2. Amount Financed:
- The amount left to be financed after the down payment is made is:
[tex]\[
y - 0.08y = 0.92y
\][/tex]
3. Installment Agreement:
- Adam agrees to make monthly payments of [tex]\( x \)[/tex] dollars for 18 months.
- The total amount paid through these monthly installments is:
[tex]\[
18x
\][/tex]
4. Finance Charge:
- The finance charge is defined as the total amount paid through installments minus the amount that was financed.
- Therefore, the expression for the finance charge is:
[tex]\[
\text{Finance Charge} = \text{Total Installments Paid} - \text{Amount Financed}
\][/tex]
- Substituting the values, we get:
[tex]\[
\text{Finance Charge} = 18x - 0.92y
\][/tex]
Thus, the correct expression representing Adam's finance charge is:
[tex]\[
18x - 0.92y
\][/tex]
Reviewing the given answer choices:
- A. [tex]\(0.8y\)[/tex]
- B. [tex]\(18y\)[/tex]
- C. [tex]\(18x - 0.92y\)[/tex]
- D. [tex]\(18x - 0.08y\)[/tex]
- E. [tex]\(18y - 0.92x\)[/tex]
The correct answer is:
[tex]\[
\boxed{3}
\][/tex]
