**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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