Problem Application

Question

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 $80, and the cost of labor to manufacture a trail bike is $60. During a week in which the company has budgeted $1,900 for materials and $2,700 for labor, how many mountain bikes does the company plan to manufacture?

Answer 1

Let x = mountain bikes

Let y = trail bikes

The cost of materials: $60x + $40y = $1900 - equation 1

The cost of labor: $80x + $60y = $2700 - equation 2

This creates a system of linear equations that can be solved by substitution, elimination or graphically.

A. Multiply Equation 1 by 8 and Multiply equation 2 by -6

480x + 320y = 15,200

-480x - 380y = -16,200

B. Add the two equations together and solve

0x - 40y = -1000 Divide both sides by -40

y = 25

C. Substitute y = 25 into Equation 1

60x + 40 (25) = 1900 Distribute

60x + 1000 = 1900. Subtract 1000 from both sides

60x = 900. Divide by 60 on both sides

x = 15

Therefore, the number of mountain bikes = 15 and the number of trail bikes = 25