Question

worksheet algebra iunit
2.4 car prices
directions: find 1 classmate to work with, if possible. if you have ever purchased something, you have probably paid a sales tax. a car purchase also involves a sales tax. car buyers pay not only the price of a car, but also a tax that is a certain percentage of the car price. car dealerships also often charge their customers various fees. in this activity, you will now write equations to describe the relationship between the price of the car, the tax, a fee, and the total price.
task statement: the tax on the sale of a car in michigan is 6%. at a dealership in ann arbor, a car purchase also involves $120 in miscellaneous charges.

1. there are several quantities in this situation: the original car price, sales tax, miscellaneous charges, and total price. write an equation to describe the relationship between all the quantities when:

a. the original car price is $9,500.
b. the original car price is $14,699.
c. the total price is $22,480.
d. the original price is p.

1. how would each equation you wrote change if the tax on car sales is r% and the miscellaneous charges are m dollars?

Explanation:

Step1: Define variables

Let $P$ be the original car - price, $T$ be the sales tax, $M$ be the miscellaneous charges, and $C$ be the total price. The sales tax $T$ is calculated as a percentage of the car price. Given the tax rate is $6\%=0.06$, and $M = 120$. So, $T=0.06P$ and $C=P + T+M=P + 0.06P+120 = 1.06P + 120$.

Step2: Solve for part a

When $P = 9500$, $C=1.06\times9500+120$.
$C = 1.06\times9500+120=10070 + 120=10190$.

Step3: Solve for part b

When $P = 14699$, $C=1.06\times14699+120$.
$C=1.06\times14699+120=15580.94+120 = 15700.94$.

Step4: Solve for part c

If $C = 22480$, then $22480=1.06P + 120$.
First, subtract 120 from both sides: $22480−120 = 1.06P$, so $22360 = 1.06P$.
Then, divide both sides by 1.06: $P=\frac{22360}{1.06}=21094.34$.

Step5: Solve for part d

The general equation when the original price is $p$ is $C = 1.06p+120$.

Step6: Solve for part 2

If the tax rate is $r\%=\frac{r}{100}$ and miscellaneous charges are $m$ dollars, the equation for the total price $C$ in terms of the original price $P$ is $C=P+\frac{r}{100}P + m=(1 + \frac{r}{100})P+m$.

Answer:

a. $C = 1.06\times9500+120 = 10190$
b. $C = 1.06\times14699+120=15700.94$
c. $P=\frac{22480 - 120}{1.06}=21094.34$
d. $C = 1.06p+120$

1. $C=(1 + \frac{r}{100})P+m$