Sales Tax: What is it and How to Add it (Charge it) to the Listed Selling Prices (Before Tax)

The Sales Tax is a consumption tax imposed by states, counties or/and cities and municipalities on the sale of goods and services, in the U.S.
Its equivalent in Europe is the Value Added Tax (VAT) and in Canada, the Goods and Services Tax (GST - HST in provinces where the provincial and federal taxes have been harmonized).
The sales tax is paid by the final consumer to the retailer at the point of sale as a percentage of the selling price of the sold good or service.
This percentage, called the Sales Tax Rate, varies from state to state, in California for example there is a general sales tax rate of around 6%.
To continue our example, cities and/or municipalities of California are also allowed to collect their own sales tax with rates ranging up to 1.75%. So a combined sales tax rate could build up to 7.75% or even more if we also add the individual county sales tax rate...
6.5% is the lowest possible sales tax rate in California, in the city of Los Angeles.
The sales tax amount paid for by the final consumer is then transfered by the retailer to the state, county or/and municipality.
A significant volume of documentation is gathered in order to determine which economic entity is ultimately liable for charging the end users the sales tax along with the price of sold items or services.

Let's say that a farmer sells apples to a company that produces cider.
To avoid paying the sales tax, the cider maker must obtain a resale certificate from the government saying that it is not the end user.
The cider maker then sells its product on to a retail store, which it will charge the final customer the sales tax along with the price of cider.

Let's say that a person who lives in an area where the sales tax rate is 5% bought some cider for $50 dollars, that person would have to pay:
5% × $50 = ⁵/₁₀₀ × $50 = ^$250/₁₀₀ = $2.5 dollars in sales tax.
The total bill containing the sales tax would be in the end: $50 dollars + $2.5 dollars = $52.5 dollars.

"Sales tax amount" = "Sales tax rate%" × "Price without sales tax"
"Sales tax charged price"
- = "Price without sales tax" + "Sales tax amount"
- = "Price without sales tax" + "Sales tax rate%" × "Price without sales tax"
- = (1 + "Sales tax rate%") × "Price without sales tax"

Example 1: If "Sales tax rate" is 5% and we charge the sales tax on a 500 dollar "Price without sales tax":
"Sales tax amount"
- = "Sales tax rate%" × "Price without sales tax"
- = 5% × 500
- = ⁵/₁₀₀ × 500
- = 5 × 5
- = 25;
"Sales tax charged price"
- = "Price without sales tax" + "Sales tax amount"
- = 500 + 25
- = 525;

Example 2: If "Sales tax rate" is 6.5% and we charge the sales tax on a 700 dollar "Price without sales tax":
"Sales tax amount"
- = "Sales tax rate%" × "Price without sales tax"
- = 6.5% × 700
- = ^6.5/₁₀₀ × 700
- = 6.5 × 7
- = 45.5;
"Sales tax charged price"
- = "Price without sales tax" + "Sales tax amount"
- = 700 + 45.5
- = 745.5;

Example 3: If "Sales tax rate" is 10.5% and we charge the sales tax on a 1,700 dollar "Price without sales tax":
"Sales tax amount"
- = "Sales tax rate%" × "Price without sales tax"
- = 10.5% × 1,700
- = ^10.5/₁₀₀ × 1,700
- = 10.5 × 17
- = 178.5;
"Sales tax charged price"
- = "Price without sales tax" + "Sales tax amount"
- = 1,700 + 178.5
- = 1,878.5;