**A motel charges a $100 flat fee per one night of stay plus 8.5% tax. Before tax, senior citizens receive a 20% discount, and children under 10 receive a 15% discount. If the motel wishes to collect at least $1,000 per day while having an average of**

*x*children under 10,*y*adults, and*z*senior citizens staying each night, which inequality shows the average daily total collected by the motel?

A. 100(0.085)

**[**1.085*x*+*y*+ 1.080*z***]**≥ 1000
B. 100(1.085)

**[**0.85*x*+*y*+ 0.80*z***]**≤ 1000
C. 100(1.085)

**[**0.85*x*+*y*+ 0.80*z***]**≥ 1000
D. 100(0.085)

**[**0.85*x*+*y*+ 0.80*z***]**≥ 1000
A senior citizen gets a 20% discount, so his
rate is 100(1 – 0.20) = 100(0.80) per night of stay. After tax, a senior
citizen will pay 100(0.80)(1 + 0.085) = 100(0.80)(1.085) dollars per night. Thus
the motel will receive 100(0.80)(1.085)

*z*from senior citizens if*z*senior citizens stay per night. An adult gets no discount, so they will pay 100(1 + 0.085) = 100(1.085) dollars per night. A total of 100(1.085)*y*is collected per night by the motel if*y*adults stay per night. A child receives a 15% discount, so his rate including tax is 100(1 – 0.15)(1 + 0.085) = 100(0.85)(1.085) dollars per night. The motel will collect 100(0.85)(1.085)*x*if*x*children stay per night. Thus the total collected by the motel for*x*children,*y*adults, and*z*senior citizens staying for the night is 100(0.85)(1.085)*x*+ 100(1.085)*y*+ 100(0.80)(1.085)*z*= 100(1.085)**[**0.85*x*+*y*+ 0.80*z***]**dollars. Since this sum must be at least 1000 dollars, it must be greater than or equal to 1000. Thus the correct answer is (C).
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