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Suzanne has purchased a car with a list price of [tex]$\$[/tex]23,860[tex]$. She traded in her previous car, which was a Dodge, and received $[/tex]85\%[tex]$ of the listed trade-in price for her car. She was also responsible for $[/tex]8.11\%[tex]$ sales tax, a $[/tex]\[tex]$1,695$[/tex] vehicle registration fee, and a [tex]$\$[/tex]228[tex]$ documentation fee. If Suzanne makes a monthly payment of $[/tex]\[tex]$455.96$[/tex], which of the following was her original car?

\begin{tabular}{|l|l|l|l|l|l|}
\hline \multicolumn{5}{|c|}{Dodge Cars in Good Condition} \\
\hline Model/Year & 2004 & 2005 & 2006 & 2007 & 2008 \\
\hline Viper & [tex]$\$[/tex]7,068[tex]$ & $[/tex]\[tex]$7,225$[/tex] & [tex]$\$[/tex]7,626[tex]$ & $[/tex]\[tex]$7,901$[/tex] & [tex]$\$[/tex]8,116[tex]$ \\
\hline Neon & $[/tex]\[tex]$6,591$[/tex] & [tex]$\$[/tex]6,777[tex]$ & $[/tex]\[tex]$6,822$[/tex] & [tex]$\$[/tex]7,191[tex]$ & $[/tex]\[tex]$7,440$[/tex] \\
\hline Intrepid & [tex]$\$[/tex]8,285[tex]$ & $[/tex]\[tex]$8,579$[/tex] & [tex]$\$[/tex]8,699[tex]$ & $[/tex]\[tex]$9,030$[/tex] & [tex]$\$[/tex]9,121[tex]$ \\
\hline Dakota & $[/tex]\[tex]$7,578$[/tex] & [tex]$\$[/tex]7,763[tex]$ & $[/tex]\[tex]$7,945$[/tex] & [tex]$\$[/tex]8,313[tex]$ & $[/tex]\[tex]$8,581$[/tex] \\
\hline
\end{tabular}

a. 2004 Intrepid
b. 2008 Neon
c. 2005 Viper
d. 2007 Dakota



Answer :

GinnyAnswer
To determine which car Suzanne originally had, we'll analyze each potential trade-in value and the effect it has on her total cost and monthly payments. Here's a step-by-step process to solve the problem:

1. List Price of New Car: [tex]\( \$23,860 \)[/tex]
2. Sales Tax Rate: [tex]\( 8.11\% \)[/tex]
3. Registration Fee: [tex]\( \$1,695 \)[/tex]
4. Documentation Fee: [tex]\( \$228 \)[/tex]
5. Monthly Payment Amount: [tex]\( \$455.96 \)[/tex]
6. Number of Monthly Payments: [tex]\( 48 \)[/tex]
7. Trade-in Value Percentage: [tex]\( 85\% \)[/tex]

First, calculate the total amount Suzanne will pay over 48 months:
[tex]\[ 48 \times 455.96 = \$21,886.08 \][/tex]

We need to identify which car's trade-in value, when adjusted and subtracted from the list price, will result in a total payment of [tex]\( \$21,886.08 \)[/tex] over 48 months.

We start by calculating the total cost for each potential car model by following these steps:

1. Calculate the adjusted trade-in value ([tex]\(85\%\)[/tex] of its listed value).
2. Subtract this adjusted trade-in value from the new car's list price to get the cost before taxes.
3. Calculate sales tax on the cost before taxes.
4. Add the registration fee and documentation fee to the cost before taxes.
5. Compare the resulting total cost with the value [tex]\(\$21,886.08\)[/tex].

Let's perform these calculations for each potential car:

### Option a: 2004 Intrepid (\[tex]$8,285) 1. Adjusted Trade-in Value: \[ 8285 \times 0.85 = 7042.25 \] 2. Cost Before Taxes: \[ 23860 - 7042.25 = 16817.75 \] 3. Sales Tax: \[ 16817.75 \times 0.0811 = 1363.92 \] 4. Total Cost: \[ 16817.75 + 1363.92 + 1695 + 228 = 20104.67 \] ### Option b: 2008 Neon (\$[/tex]7,440)
1. Adjusted Trade-in Value:
[tex]\[ 7440 \times 0.85 = 6324 \][/tex]
2. Cost Before Taxes:
[tex]\[ 23860 - 6324 = 17536 \][/tex]
3. Sales Tax:
[tex]\[ 17536 \times 0.0811 = 1422.88 \][/tex]
4. Total Cost:
[tex]\[ 17536 + 1422.88 + 1695 + 228 = 20881.88 \][/tex]

### Option c: 2005 Viper (\[tex]$7,225) 1. Adjusted Trade-in Value: \[ 7225 \times 0.85 = 6141.25 \] 2. Cost Before Taxes: \[ 23860 - 6141.25 = 17718.75 \] 3. Sales Tax: \[ 17718.75 \times 0.0811 = 1436.46 \] 4. Total Cost: \[ 17718.75 + 1436.46 + 1695 + 228 = 21078.21 \] ### Option d: 2007 Dakota (\$[/tex]8,313)
1. Adjusted Trade-in Value:
[tex]\[ 8313 \times 0.85 = 7066.05 \][/tex]
2. Cost Before Taxes:
[tex]\[ 23860 - 7066.05 = 16793.95 \][/tex]
3. Sales Tax:
[tex]\[ 16793.95 \times 0.0811 = 1362.94 \][/tex]
4. Total Cost:
[tex]\[ 16793.95 + 1362.94 + 1695 + 228 = 20079.89 \][/tex]

Now, we compare the total costs to the amount Suzanne is paying over 48 months:

[tex]\[ 21886.08 \][/tex]

Only "none of these options" results in matching the total monthly payment over 48 months. Hence, there is no car matching the given trade-ins and conditions.

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