System of Equations.

Question

An electronics company produces transistors, resistors, can computer chips. Each transistor requires 3 units of copper, 1 unit of zinc, and 2 unites of glass. Each resistor requires 3, 2, and 1 unite of the three materials, and each computer chip requires 2, 1, and 2 units of these materials, respectively. How many of each product can be made with the follwing amounts of materials? 810 units of copper, 419 of zinc, and 490 of glass

Answer 1

You have 810 units of copper. 3 units are used in transistors, 3 in resistors and 2 in chips. So,

3t + 3r + 2c = 810

 

You have 419 units of zinc, 1 for transistors, 2 for resistors and 1 for chips. So,

t + 2r + c = 419

 

Likewise for glass

2t + 2r + 2c = 490

 

That last equation makes this easy to solve. If you double the second equation and then subtract the third equation, you can solve for r.

 

2t + 4r + 2c = 838

2t + 2r + 2c = 490   subrtract to get

 

2r = 348

r = 174

 

Go back and substitute this in and finish the problem.

Hope this helped