SOLUTION: A MACHINE IN A POTTERY FACTORY TAKES 3 MINUTES TO FORM A BOWL AND 1 MINUTE TO FORM A PLATE. The material for a bowl cost 25 cents and material for a plate costs 20 cents . If the m

Question 943192: A MACHINE IN A POTTERY FACTORY TAKES 3 MINUTES TO FORM A BOWL AND 1 MINUTE TO FORM A PLATE. The material for a bowl cost 25 cents and material for a plate costs 20 cents . If the machine runs for 8 hours (480 minutes) and exactly 44 dollars is available to spend on materials, how many bowls and plates can be produced?
So far I have 0.25x+0.20y=44 and 3x+y=8 is am I missing another equation?
Found 2 solutions by josmiceli, macston:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
You don't say what and mean
I would define them as:
Let = the number of minutes the machine
spends making bowls
Let = the number of minutes the machine
spends making plates
-----------------------
Then my equations would be:
(1) ( changing dollars to cents )
(2)
---------------------
(1)
(1)
Multiply both sides of (2) by and
subtract (2) from (1)
--------------------
(1)
(2)
-----------------------

and
(2)
(2)
----------------------

It looks like the machine makes
148 bowls and 34 plates
( can't make fractions of them )
check:
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
OK
---------
Check my math, assumptions, and conclusions
carefully. I have been WAY off base before.

Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
Let P=Plates and B=bowls
0.25B+.20P=44; 3B+P=480 (This equation was your problem: convert all to same units)
Solve second equation for P
P=480-3B
Substitute in first
0.25B+(.2(480-3B))=44
0.25B+96-0.6B=44
96-.35B=44 Subtract 44 from each side
96-44-0.35B=0 add .35B to each side
52=0.35B divide each side by 0.35
(52/.35)=.35B/.35
148.6=B Number of bowls is 148.6
P=480-3(148.6)= 34.2 Number of plates is 34.2
CHECK
Material
0.25B+0.20P=44
0.25(148.6)+0.20(34.2)=44
37.15+6.84=44
43.99=44 (discrepancy due to rounding)
Time
3(148.6)+34.2=480
445.8+34.2=480
480=480

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