SOLUTION: Keith works at coffee shop, where a 10 oz cup of coffee costs $1.05, a 14oz cup of coffee costs $1.35, and a 20 oz cup of coffee costs $1.65. During a busy day, Keith served 34 cup

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Question 130046: Keith works at coffee shop, where a 10 oz cup of coffee costs $1.05, a 14oz cup of coffee costs $1.35, and a 20 oz cup of coffee costs $1.65. During a busy day, Keith served 34 cups of coffee, emptying five 96 oz pots while collecting a total of $45. How many cups of each size did Keith fill?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
a= number of 10 oz cups
b= number of 14 oz cups
c= number of 20 oz cups
105a+%2B+135b+%2B+165c+=+4500
21a+%2B+27b+%2B+33c+=+900
(1) 7a+%2B+9b+%2B+11c+=+300
(2) a+%2B+b+%2B+c+=+34
(3) 10a+%2B+14b+%2B+20c+=+5%2A96
From (2):
(4) c+=+34+-+a+-+b
Substitute this in (1)
(1) 7a+%2B+9b+%2B+11c+=+300
7a+%2B+9b+%2B+11%2A%2834+-+a+-+b%29+=+300
7a+%2B+9b+%2B+374+-+11a+-+11b+=+300
-4a+-+2b+=+-+74
2a+%2B+b+=+37
(5) b+=+37+-+2a
Substitute (4) and (5) in (3)
(3) 10a+%2B+14b+%2B+20c+=+5%2A96
10a+%2B+14%2A%2837+-+2a%29+%2B+20%2A%2834+-+a+-+b%29+=+5%2A96
10a+%2B+518+-+28a+%2B+680+-+20a+-+20b%29+=+5%2A96
-38a+-+20b+=+480+-+518+-+680
38a+%2B+20b+=+718
substitute (5) for b
38a+%2B+20%2A%2837+-+2a%29++=+718
38a+%2B+740+-+40a+=+718
-2a+=+-22
a+=+11
(5) b+=+37+-+2a
b+=+37+-+2%2A11
b+=+15
(4) c+=+34+-+a+-+b
c+=+34+-+11+-+15
c+=+8
Keith filled 11 10 oz cups, 1514 oz cups,
and 8 20 oz cups
check answer:
(1) 7a+%2B+9b+%2B+11c+=+300
7%2A11+%2B+9%2A15+%2B+11%2A8+=+300
77+%2B+135+%2B+88+=+300
300+=+300
(2) a+%2B+b+%2B+c+=+34
11+%2B+15+%2B+8+=+34
34+=+34
(3) 10a+%2B+14b+%2B+20c+=+5%2A96
10%2A11+%2B+14%2A15+%2B+20%2A8+=+480
110+%2B+210+%2B+160+=+480
480+=+480
OK