Question

The price of the new car is $\mathrm{\$}29,990$. If the sales tax rate is $6.5\mathrm{\%}$ , then how much sales tax is being charged? What is the total cost for the car including tax?

Answer 1

Hint: In this question, we have to find the sales tax and the total cost of a car. Thus, we will use the percentage formula and the basic mathematical rule to get the solution. First, we will let the sales tax be equal to x. After that, we will multiply the price of a new car and the sales tax rate, to get the value of x. Then, we will add the price of the new car and the sales tax value to get the value of total cost of the car, which is the required solution for the problem.

Complete step by step solution:
According to the question, we have to find the sales tax and the total cost from the given problem
Thus, we will use the percentage method and the mathematical rule to get the solution.
Let us suppose the value of sales tax is equal to x ---- (1)
The price of the new car is $\mathrm{\$}29,990$ ------ (2)
Sales tax rate is equal to $6.5\mathrm{\%}$ ------- (3)
Now, we know that the sales tax rate is given in the form of percentage from equation (3), thus we will remove the percentage, by dividing the tax rate by 100, that is
$\Rightarrow 6.5\mathrm{\%}={\displaystyle \frac{6.5}{100}}$
On further solving the right hand side of the above equation, we get
$\Rightarrow 6.5\mathrm{\%}={\displaystyle \frac{65}{1000}}$ ------- (4)
Now, for sales tax, we will multiply the price of the new car and the sales tax rate, we get
$\Rightarrow \text{sales tax}=\text{price of new car}\times \text{sales tax rate}$
Now, put the value of equation (1), (2), and (4) in the above equation, we get
$\Rightarrow x=\mathrm{\$}29990\times {\displaystyle \frac{65}{1000}}$
$\Rightarrow x={\displaystyle \frac{\mathrm{\$}1949350}{1000}}$
On further simplification, we get
$\Rightarrow x=\mathrm{\$}1949.35$ ------- (5)
Now, for the total cost of the car including tax, it is equal to the sum of the price of new car and the price of sales tax, we get
$\Rightarrow \text{total cost=new price+sales tax}$
On putting the value of equation (2) and (5) in the above equation, we get
$\Rightarrow \text{total cost}=\mathrm{\$}29990+\mathrm{\$}1949.35$
$\Rightarrow \text{total cost}=\mathrm{\$}32939.35$
Therefore, for the given problem, price of sales tax is equal to $\mathrm{\$}1949.35$ and total cost of the car including tax is equal to $\mathrm{\$}32939.35$.

Note: While solving this problem, do mention all the steps properly to avoid confusion and mathematical error. Do not forget to remove the percentage by dividing it by 100. Always put the standard unit sign in the solution, to get an accurate answer.