SOLUTION: Manufacturing: a company manufactures both mountain bikes and trail bikes. The cost of materials for a mountain bike is $70, and the cost of materials for a trail bike is $50. The
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Question 164615: Manufacturing: a company manufactures both mountain bikes and trail bikes. The cost of materials for a mountain bike is $70, and the cost of materials for a trail bike is $50. The cost of labor to manufacture a mountain bike is $80, and the cost of labor to manufacture a trail bike is $40. During a week in which the company has budgeted $2500 for materials and $2600 for labor, how many mountain bikes does the company plan to manufacture?
What I need is what steps to take to solve this problem.
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
let x = number of mountain bikes to be manufactured.
let y = number of trail bikes to be manufactured.
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total cost of material is $2500.
cost of material for mountain bike is 70.
cost of material for trail bike is 50.
equation for total material is:
70*x + 50*y = 2500
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total cost of labor is $2600.
cost of labor for mountain bike is 80.
cost of labor for trail bike is 40.
equation for total labor is:
80*x + 40*y = 2600
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solve these equations simultaneously.
70*x + 50*y = 2500 (first equation)
80*x + 40*y = 2600 (second equation)
multiply both sides of first equation by 4 and multiply both sides of second equation by 5. this will allow you to eliminate the y from the equation so you can solve for x.
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280*x + 200*y = 10000
400*x + 200*y = 13000
subtract first equation from second equation.
120*x = 3000
divide both sides by 120.
x = 25
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substitute 25 for x in first equation.
70*(25) + 50*y = 2500
1750 + 50*y = 2500
subtract 1750 from both sides
50*y = 750
y = 15
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substitute 25 for x and 15 for y in second equation.
80*25 + 40*15 = 2600
2000 + 600 = 2600
2600 = 2600
x = 25 and y = 15 are good in second equation.
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answer is:
x = 25
y = 15
number of mountain bikes to manufacture = 25
number of trail bikes to manufacture = 15
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