Question 414326
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Hi
total number of people are 546
Letting x and (546-x)represent the number of adults and children respectively...
 12.00x + 5.50(546-x) = $5115.50
            6.50x = 5115.50 - 5.50*546 
                x = 325, the number of adult plates.  221 children plates

CHECKING our Answer***
 $12*325 + $5.50*221 = $5115.50