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Question 534358: How do I use two variables and two equations to solve this problem. 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 and exactly $44 is spent for material, how many bowls and plates can be produced? How do I set it up?
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! let number of bowls be x
and plates be y
time taken
3x+2y= 480
Money spent
0.25x+0.2y = 44
multiply by 100 to eliminate the decimals
25x+20y=4400
bowls x numbers , Price = $3.00
plates y numbers , Price = $9.00
Total 345
3 x + 2 y = 480 .............1
25 x + 20 y = 4400 .............2
Eliminate y
multiply (1)by -10
Multiply (2) by 1
-30 x -20 y = -4800
25 x 20 y = 4400
Add the two equations
-5 x = -400
/ -5
x = 80
plug value of x in (1)
3 x + 2 y = 480
240 + 2 y = 480
2 y = 480 -240
2 y = 240
y = 120
bowls 80 numbers
plates 120 numbers
m.ananth@hotmail.ca
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