SOLUTION: 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

Algebra ->  Matrices-and-determiminant -> SOLUTION: 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       Log On


   

Question 358501: 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 and how many trail bikes does the company plan to manufacture?
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
set up your equation, you need two equations since there are two unknowns
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Let M=number of Mountain bikes manufactured
Let T=number of trail bikes manufactured
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There are two constraints (two equations)
eq 1 (material): 70*M+50*T=2500
eq 2 (labor): 80*M+40*T=2600
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reduce, simplify the equations
eq 3: 7M+5T=250 (divide both sides of eq 1 by 10)
eq 4: 10M+5T=325 (divide both sides of eq 2 by 8)
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subtract eq 3 from eq 4
3M=75
M=75/3=25
substitute M=25 into one of the original equations eq 1 or eq 2
and solve for T
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70*(25)+50*T=2500
T=(2500-1750)/50=75/5=15
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answer highlight%28M=25%29 and highlight%28T=15%29
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Note
you should substitute these values in both original equations eq1 & eq2 to validate the answer, I'll leave that to you