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 $30, whereas the cost of materials fo

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Question 273554: A company manufactures both liquid crystal display (LCD) and cathode ray tube (CRT) color monitors. The cost of materials for a CRT monitor is $30, whereas the cost of materials for an LCD monitor is $130. The cost of labor to manufacture a CRT monitor is $80, whereas the cost of labor to manufacture an LCD monitor is $130. During a week when the company has budgeted $7910 for materials and $10260 for labor, how many LCD monitors does the company plan to manufacture?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
cost of CRT materials = $30
cost of LCD materials = $130
cost of CRT labor = $80
cost of LCD labor = $130
total cost of materials = $7910
total cost of labor = 10260

let x = number of CRT
let y = numbe4r of LCD

equation for material is:

30x + 130y = 7910

equation for labor is:

80x + 130y = 10260

you need to solve these 2 equations to get your answer.

the equations are: 
                     30x + 130y = 7910
                     80x + 130y = 10260

subtract first equation from second to get:

50x = 2350

divide both sides of this equation by 50 to get:

x = 47

substitute for x in first equation to get:

30x + 130y = 7910 becomes:
30*47 + 130y = 7910 which becomes:
1410 + 130y = 7910
subtract 1410 from both sides to get:
130y = 7910 - 1410
combine like terms to get:
130y = 6500
divide both sides by 130 to get:
y = 50

you have x = 47 and y = 50

substitute in both original equations to see that these values solve both of them at the same time.

original equations are: 
                     30x + 130y =  7910
                     80x + 130y = 10260

after substitution they become: 
                     30*47  + 130*50  =  7910
                     80*47  + 130*50  = 10260

simplify to get: 
                     1410  + 6500  =  7910
                     3760  + 6500  = 10260

both these equations are true confirming the values for x and y are good.

x is the number of CRT
y is the number of LCD

answer to the question is that 50 LCD monitors are being planned to be manufactured during a week that the company has budgeted 7910 for materials and 10260 for labor.