SOLUTION: The St. Mark Community babecue served 250 dinners. Achilds plate cost $3.50 and an adult plate is $7.00. A total of $1347.50 was collected. How many of each type of plate was serve

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Question 309710: The St. Mark Community babecue served 250 dinners. Achilds plate cost $3.50 and an adult plate is $7.00. A total of $1347.50 was collected. How many of each type of plate was served? Please show work. Thanks
Found 2 solutions by alicealc, rfer:
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
child's plate = c
adult's plate = a

(1) c + a = 250
(2) 3.5c + 7a = 1347.50
multiply equation (1) by 7
(1) 7c + 7a = 1750
(2)3.5c+ 7a = 1347.50
---------------------- (-)
3.5c = 402.5
c = 402.5/3.5 = 4025/35 = 115

c + a = 250
115 + a = 250
a = 250 - 115 = 135

so, child's plates reserved = 115 plates
adult's plate reserved = 135 plates

Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
c+a=250 c=250-a
3.5c+7a=1347.5
3.5(250-a)+7a=1347.5
875-3.5a+7a=1347.5
3.5a=472.5
a=135 adults
c=250-135
c=115 children
proof
3.5*115+7*135=$
402.5+945=$1347.50