The sales tax on an item with a retail price of $972 is $68.04.Create a variational model that gives the retail price,y,in terms of the sales tax,x,and use it to determine the retail price of an item that has a sales tax of $82.62.
A)$1182.28
B)$1151.92
C)$1180.29
D)$1192.52
E)$1124.60

Question

Quizplus · Accepted Answer

Let's define the sales tax rate as $r$. Then, we know that:

$r = \dfrac{68.04}{972} \approx 0.07$

This means that the sales tax rate is approximately 7%.

We can set up a variational model as:

$y = (1+r)x$

where $y$ is the retail price, $x$ is the sales tax, and $r$ is the sales tax rate.

Plugging in the values we know, we get:

$y = (1+0.07)(82.62) \approx 1180.29$

Therefore, the retail price of an item with a sales tax of $82.62 is approximately $1180.29.

The best choice is C.

The Sales Tax on an Item with a Retail Price