Question

A department store in your hometown charges 9.75% tax; the stores location in your cousins hometown only charges 7.75% tax. If a shoppers pre tax receipt is between $11.57 and $81.43, write and graph a compound inequality that describes the differences in taxes paid for the two locations (to the nearest cent).

Answer 1

The compound inequality would be
0.23≤x≤1.63.

The graph would have a number line marked at least from 0.23 to 1.63; both of these numbers would have a filled in circle over them, and the area of the line between them would be shaded.

We must find the amount of tax for each city and each purchase amount:
9.75%=9.75/100 = 0.0975
0.0975(11.57) = 1.13
0.0975(81.43) = 7.94

7.75% = 7.75/100 = 0.0775
0.0775(11.57) = 0.90
0.0775(81.43) = 6.31

To find the differences in the tax amounts, we subtract:
1.13 - 0.90 = 0.23
7.94 - 6.31 = 1.63