Answer:
$642
Step-by-step explanation:
How to calculate the amount of sales tax?
Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
Multiple the pre-tax value by the newly calculated decimal value in order to find the cost of the sales tax.
Add the sales tax value to the pre-tax value to calculate the total cost.
Calculating sales tax at time of purchase:
In order to calculate the sales tax of an item, we need to first multiply the pre-tax cost of the item by the sales tax percentage after it has been converted into a decimal. Once the sales tax has been calculated it needs to be added to the pre-tax value in order to find the total cost of the item. Let's start by working with an example. If a magazine costs $2.35 and has a 6% sales tax, then what is the total cost of the item. First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.
6%→0.06
Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.
\textup{Sales tax}=0.06\times\$2.35
\textup{Sales tax}=\$0.141
Round to two decimal places since our total is in dollars and cents.
\textup{Sales tax}=\$0.14
Last, add this value to the pre-tax value of the item to find the total cost.
\textup{Total cost}=\textup{Pre-tax value}+\textup{Sales tax}
\textup{Total cost}=\$2.35+\$0.14
\textup{Total cost}=\$2.49
Calculating the sales tax percentage of a total:
If we are given the total cost of an item or group of items and the pre-tax cost of the good(s), then we can calculate the sales tax percentage of the total cost. First, we need to subtract the pre-tax value from the total cost of the purchase. Next, we need to create a ratio of the sales tax to the pre-tax cost off the items. Last, we need to create a proportion where the pre-tax cost is related to 100% and solve for the percentage of the sales tax. Let's start by working through an example. If a person pays $245.64 for groceries that cost $220.00 pre tax, then what is the sales tax percentage for the items.
First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.
\textup{Sales tax}=\textup{Total cost}-\textup{Pre-tax value}
\textup{Sales tax}=\$245.64-\$220.00
\textup{Sales tax}=\$25.64
Next, create a ratio of the sales tax to the pre-tax cost of the items.
\frac{\textup{Sales tax}}{\ \textup{Pre-tax value}} = \frac{\$25.64}{\$220.00}
Last, create a proportion where the pre-tax value is proportional to 100% and solve for the percentage of sales tax.
\frac{\$25.64}{\$220.00}=\frac{\textup{Sales tax percentage}}{100\%}
Cross multiply and solve.
\$220.00\times\textup{Sales tax percentage}=\$25.64\times 100\%
\$220.00\times\textup{Sales tax percentage}=\$2564.00
Isolate the sales tax percentage to the left side of the equation by dividing each side by the pre-tax value.
\frac{\$220.00\times\textup{Sales tax percentage}}{\$220.00}=\frac{\$2564.00}{\$220.00}
\textup{Sales tax percentage}=11.6545455\%
Round to two decimal places since our answer is in dollars and cents.
\textup{Sales tax percentage}=11.65\%
Last, we can check this answer by calculating the sales tax percentage of the total as seen previously.
First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.
11.6545455%→0.116545455
Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.
\textup{Sales tax}=0.116545455\times\$220.00
\textup{Sales tax}=\$25.6400001
Round to two decimal places since our total is in dollars and cents.
\textup{Sales tax}=\$25.64
Last, add this value to the pre-tax value of the item to find the total cost.
\textup{Total cost}=\textup{Pre-tax value}+\textup{Sales tax}
\textup{Total cost}=\$220.00+\$25.64
\textup{Total cost}=\$245.64
Our answers check out; therefore they are correct. Now, let's use this information to solve the given problem.
Solution:
First, calculate the amount of sales tax by multiply the percent tax times the total cost:
0.07×600 =42
Next, add the amount of tax to the price of the computer:
600+42=642
. Simplifying a bit we get 
and 
. Taking the square root of that and considering the principle root only, x = 39.2, second choice down.