how to write and graph a compound inequality that describes the difference in taxes

Question

A department store in your hometown charges 9.75% tax; the store's location in your cousin's hometown only charges 7.25% tax. If a shoppers tax receipt is between $11.57 and $81.43, write and graph a compound inequality that describes the difference in taxes paid for the two locations (to the nearest cent).

Answer 1

Let x be the cost and we know that pre-tax receipt is between $11.57 and $81.43 thus

11.57≤ x ≤ 81.43

Let y be the difference in taxes then

11.57*(9.75/100 - 7.25/100) ≤ y ≤ 81.43*(9.75/100 - 7.25/100)

11.57*(0.0975 - 0.0725) ≤ y ≤ 81.43*(0.0975 - 0.0725)

11.57*0.0250 ≤ y ≤ 81.43*0.0250

0.28925 ≤ y ≤ 2.03575

Compound inequality of difference in taxes is

0.28925 ≤ y ≤ 2.03575

To the nearest cent is

0.29 ≤ y ≤ 2.04

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