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Prices with and Without Taxes

Sales tax is a tax on goods and services that you purchase. Many countries outside of the US use value-added tax (VAT) instead of sales tax. VAT is applied at every level of the supply chain, whereas sales tax is only applied to the final, retail sale price.

Sales taxes vary from state to state. For these exercises, let’s assume that the sales tax is $5$ %. People say that “the sales tax rate is $5$ %”. But you should always ask yourself “ $5$ % of what?” The tax is $5$ % of the item’s price before the tax is added, not $5$ % of the price you pay at the register (the total sales price).

Rule

Finding the Total Sales Price with $5 %$ Tax

The tax on goods is $5$ % of the what the price is before tax is added. Recall that $5 % = 0.05$ . This means that

\begin{array}{l} Sales price = 1.05 \times price before tax \end{array}

\begin{array}{l} Sales price & = price before tax + 0.05 \times price before tax \\ = 1.05 \times price before tax \end{array}

Example 1

A shopkeeper wants to sell an item at $$ 15$ before tax. How much will his customers have to pay for that item?

Sales price = 1.05 \times $ 15 = $ 15.75

Of the $ $15.75$ , the tax is

0.05 \times $ 15 = $ 0.75

That means the shopkeeper is left with

$ 15.75 - $ 0.75 = $ 15

just like he wanted.

Example 2

You continue with Example 1 and ask: What percentage of the total sales price $($ 15.75)$ is the tax $($ 0.75)$ ?

You use what you have learned about converting fractions into percentages via decimal numbers:

\frac{$ 0.75}{$ 15.75} = \frac{75}{1575} \approx 0.0475 \approx 4.75 %

That the sales tax is $4.75$ % of the sales price is true for all items with a sales tax rate of $5$ %.

Many people think that the sales tax is $5$ % of the total sales price, but that’s incorrect. Even if the tax is $5$ %, it’s only $4.75$ % of the price you end up paying.

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Activities 4

Growth Factor

Finding the Total Sales Price with 5% Tax

Finding the Total Sales Price with $5 %$ Tax