Question 1184066
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A company manufactures both mountain bikes and trail bikes. 
The cost of materials for a mountain bike is $60, and the cost of materials for a trail bike is $40. 
The cost of labor to manufacture a mountain bike is $90, and the cost of labor to manufacture a trail bike is $30. 
During a week in which the company has budgeted $1,700 for materials and $1,950 for labor, 
how many mountain bikes does the company plan to manufacture?
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<pre>
Let  m  be the number of the mountain bikes,

     t  be the number of the trail bikes.


Write equations as you read the problem

    60m + 40t = 1700    (1)    (material money) 

    90m + 30t = 1950    (2)    (labor money)


Solve by the elimination method.
Since they ask about mountain bikes, eliminate t.


For it, multiply equation (1) by 3 and multiply equation (2) by 4.
You will get
  
    180m + 120t = 5100    (3)   

    360m + 120t = 7800    (4)   


Now subtract equation (3) from equation(4)

     180m        = 7800 - 5100

     180m        =     2700

        m        =     2700/180 = 15.


<U>ANSWER</U>.  The company plans to manufacture 15 mountain bikes.
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Solved.