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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
You don't say what +x+ and +y+ mean
I would define them as:
Let +x+ = the number of minutes the machine
spends making bowls
Let +y+ = the number of minutes the machine
spends making plates
-----------------------
Then my equations would be:
(1) +25%2A%28x%2F3%29+%2B20y+=+4400+ ( changing dollars to cents )
(2) +x+%2B+y+=+480+
---------------------
(1) +25x+%2B+60y+=+13200+
(1) +5x+%2B+12y+=+2640+
Multiply both sides of (2) by +5+ and
subtract (2) from (1)
--------------------
(1) +5x+%2B+12y+=+2640+
(2) +-5x+-+5y+=+-2400+
-----------------------
+7y+=+240+
+y+=+34.286+
and
(2) +x+%2B+y+=+480+
(2) +x+=+445.714+
----------------------
+x%2F3+=+148.571+
It looks like the machine makes
148 bowls and 34 plates
( can't make fractions of them )
check:
(1) +25%2A%28x%2F3%29+%2B20y+=+4400+
(1) +25%2A148.571+%2B20%2A34.286+=+4400+
(1) +3714.28+%2B+685.72+
(1) +4400+=+4400+
and
(2) +x+%2B+y+=+480+
(2) +445.714+%2B+34.286+=+480+
(2) +480+=+480+
OK
---------
Check my math, assumptions, and conclusions
carefully. I have been WAY off base before.



Answer by macston(5194) About Me  (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