## Real World Applications – Algebra I

### Topic

Financing a Fiat

### Student Exploration

In 2012, one of the most popular cars to purchase in California was a Fiat. They advertised on their commercials their cheap monthly payments. Let’s look into what a potential car-owner would look forward to, and use two-step equations to find out the best deal.

In April, a quote was given to a potential Fiat owner based on how much they could first pay up front (called the down payment). The total cost of a Fiat is $18,408.06, including all taxes and fees. All of the following calculations are based on a 60-month pay period. If there is “zero down,” or no money paid as a down payment, based on a 60-month pay period, we can figure out how much the owner would pay per month. Let’s use the formula, \begin{align*}y = mx + b\end{align*}, and let’s assume that \begin{align*}y\end{align*} represents the total amount paid for the car, \begin{align*}m\end{align*} represents the monthly payment, \begin{align*}x\end{align*} represents the number of months the owner is paying, and \begin{align*}b\end{align*} represents the initial down payment. If there is no money down, then the equation is \begin{align*}18408.06 = (m)(60) + 0\end{align*}. This equation can be solved in one step. We divide both sides by 60, and find that the monthly payment is $306.80. Not bad, but the potential owner really wants to pay as close to $200 a month, as in what the commercial on television advertised.

To lower the monthly payment, the owner would have to initially put down money. What if the down payment was $2,000? If the owner took 60 months to pay off the car, how much is the monthly payment? Let’s use the formula to find out:

\begin{align*}Y &= mx + b\\ 18,408.06 &= (m)(60) + 2000\\ 16,408.06 &= 60m\\ \$273.47 &= m\end{align*}

What if the down payment was $5,000? How much would this car owner pay every month for 60 months?

We can also apply our understanding of percent equations to find out the percent tax on the car. We set the dollar amount of tax equal to the original sticker price of the car multiplied by the percent (which is the unknown). On the printout that a car salesperson gave, we know that the tax is $1,466.06 and the sticker price is $16,700. Our equation is,

\begin{align*}1466.06 - 16700(p)\end{align*}, and \begin{align*}p\end{align*} represents the sales tax. We solve this equation by dividing both sides by 16700, and we get \begin{align*}p = 0.0878\end{align*}.

We use our knowledge of converting this decimal to percent by multiplying this by 100. The sales tax is 8.78%.

### Extension Investigation

Try looking up a car that you would potentially purchase (either new or used). Try to find out how much you could pay every month for 60 months, knowing the total price of the car.