SOLUTION: A machine in a pottery factory takes 3 minutes to form a bowl and 2 minutes to form a plate. The material for a bowl costs $0.25 and the material for a plate costs $0.20. If the ma

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Question 1096741: A machine in a pottery factory takes 3 minutes to form a bowl and 2 minutes to form a plate. The material for a bowl costs $0.25 and the material for a plate costs $0.20. If the machine runs for 8 hours straight and exactly $44 is spent for materials, how many bowls and plates can be produced.
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of bowls produced
Let +b+ = number of plates produced
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Convert hrs to min
(1) +3a+%2B+2b+=+8%2A60+
(2) +.25a+%2B+.2b+=+44+
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(1) +3a+%2B+2b+=+480+
and
(2) +25a+%2B+20b+=+4400+
(2) +5a+%2B+4b+=+880+
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Multiply both sides of (1) by +2+
Subtract (2) from (1)
------------------------------------
(1) +6a+%2B+4b+=+960+
(2) +-5a+-+4b+=+-880+
-----------------------------
+a+=+80+
(1) +3a+%2B+2b+=+480+
Solve for +b+

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
From the condition, you have these two equations (the system of two equations)

   3*b +    2*p = 8*60      (1)    (minutes)
0.25*b + 0.20*p =   44      (2)    (dollars)


where b = # of bowls,  p = # of plates.  Simplify

   3b +  2p =  480,         (3)
  25b + 20p = 4400.         (4)


Setup is done. Solve it by any method you know. Eliminating of "p" seems to be attractive.