show all work neatly

Question

the price of a certain item is p dollar. the sales tax on items is 7%. which expressions represent the total cost of the time, in dollars after the tax has been applied?

0.07p

1.07p

p+0.07p

1+0.07p

(1+0.07)p

Answer 1

p + 0.07p

(1 + 0.07)p

1.07p

Answer 2

Hi Christabel,

So sales tax is a percentage of the bill that is added on top of the bill when you go to pay. For instance, if you had 10% sales tax and your bill was $100, it means that you will pay $100 in addition to 10% of $100, which is $10, for a total of $110.

In math terms this would be written as:

$100 + $100 * 10% tax = $110

You might notice that there is a common term of "$100" that can be factored out.

Factoring this out we get:

$100(1 + .1) = $110

now if we wanted to make this equation true for all dollar values, we could use the variable p in place of the "$100". this gives us:

p(1 + .1) = total cost

The question provided, however, uses a tax rate of 7%. We can easily substitute this value into the equation to get

p(1 + .07) = total cost

simplifying this expression gets you

1.07p = total cost

and this makes sense intuitively, since 1.07 * a number will always be 7% more than 100% of that value.

I hope that helps!