Question 1184066: 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?
Answer by ikleyn(52879)   (Show Source):
You can put this solution on YOUR website! .
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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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.
ANSWER. The company plans to manufacture 15 mountain bikes.
Solved.
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