SOLUTION: A company manufactures both liquid crystal display (LCD) and cathode ray tube (CRT) color monitors. The cost of materials for a CRT monitor is $60, whereas the cost of materials fo

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Question 1054328: A company manufactures both liquid crystal display (LCD) and cathode ray tube (CRT) color monitors. The cost of materials for a CRT monitor is $60, whereas the cost of materials for an LCD monitor is $120. The cost of labor to manufacture a CRT monitor is $90, whereas the cost of labor to manufacture an LCD monitor is $130. During a week when the company has budgeted $9720 for materials and $11580 for labor, how many LCD monitors does the company plan to manufacture?
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
set up a table as follows: 



                  x                  y         
                 CRT                LCD            total 
                
material         60                 120             = 9720
labor            90                 130             = 11580


x is equal to the number of CRT.
y is equal to the number of LCD

total material is equal to 9720.
total labor is equal to 11580.

you have two equations that need to be solved simultaneously.

they are:

60x + 120y = 9720
90x + 130y = 11580

we'll solve by elimination.

multiply both sides of the first equation by 1.5 and leave the second equation as is to get:

90x + 180y = 14580
90x + 130y = 11580

subtract the second equation from the first equation to get:

50y = 3000

solve for y to get y = 60

replace y in the first original equation with 60 and solve for x to get:
60x + 120y = 9720 becomes 60x + 7200 = 9720.
solve for x to get x = 42.

your solution is x = 42 and y = 60

this means that you will manufacture 42 CRT and 60 LCD.

your original equations of:

60x + 120y = 9720
90x + 130y = 11580

become:

60 * 42 + 120 * 60 = 9720
90 * 42 + 130 * 60 = 11580

simplify to get:

9720 = 9720
11580 = 11580

x represents the number of CRT which is equal to 42.
y represents the number of LCD which is equal to 60.

solution looks good.

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