Question

1. In New York, state sales tax rates vary by county. In Allegany County, the sales tax rate is 8 1/2%.

a. A book costs $12.99, and a video game costs $39.99. Rounded to the nearest cent, how much more is the tax on the video game than the tax on the book?

b. Using to represent the cost of an item in dollars before tax and to represent the amount of sales tax in dollars for that item, write an equation to show the relationship between and .

c. Using your equation, create a table that includes five possible pairs of solutions to the equation. Label each column appropriately.

Answer 1

A) $2.30 more.
B) y=0.085x
C) A sample table is attached, listing the values for x, the process and the value for y.

Explanation
A) The amount of tax on a $12.99 book is given by 0.085(12.99)=1.10415≈$1.10.
The amount of tax on a $39.99 video game is given by 0.085(39.99)=3.39915≈$3.40.

This gives us a difference of 3.40-1.10 = $2.30.

B) Using x as the cost before tax and y for the amount of tax, we have the equation y=0.085x.
8.5% = 8.5/100 = 0.085.  To find the amount of tax, we multiply this rate by the cost, which gives us the equation above.