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).

Question

Mathematics

Corey Frederick

23 December, 10:43

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).

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Nolan · 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