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A beverage store charges a base price of x dollars for one keg of root beer. A sales tax of a certain percentage is applied to the base price, and an untaxed deposit for the keg is added. If the total amount, in dollars, paid at the time of purchase for one keg is given by the expression 1.07x+17, then what is the sales tax, expressed as a percentage of the base price? (Fully Explained)

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AnimalPostidn

Answer:

7% is the sales tax.

Explanation:

So, our base price is x dollars:

x = base price

Now, we are given the expression 1.07x + 17

This expression can be rewritten as:

(1.00 + 0.07)x + 17

Also seen as:

(100% + 7%)x + 17

We know that 100% is the normal price, but the added 0.07 or 7% should be the sales tax of the base price.

We know this because it is a "rate" multiplying by the base price x.

Furthermore, since the percentage is above 1.00 or 100% (the rate is 107%), then the price of the keg will increase. This must be true because it is a sales tax.

The constant number 17 represents the starting price if there was no tax (or if the base price was x = 0).

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