SOLUTION: John is analyzing the cost of producing two different sensors products at an electronics company.Sensor A uses 5 grams of zinc and requires 3 hours to assemble. The total productio

Algebra ->  Finance -> SOLUTION: John is analyzing the cost of producing two different sensors products at an electronics company.Sensor A uses 5 grams of zinc and requires 3 hours to assemble. The total productio      Log On


   

Question 1154308: John is analyzing the cost of producing two different sensors products at an electronics company.Sensor A uses 5 grams of zinc and requires 3 hours to assemble. The total production cost of sensor A is $54. Sensor B uses 4 zinc but requires 5 hours to assemble. The total production cost of sensor B is $64. How much does it cost the company for gram of this type of zinc? What is the hourly labour cost at this company?
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Let cost of zinc = x dollars per gram
Let labour charge = y dollars per hour
Sensor A uses 5 gm zinc, 3 hours, costing 54. So we get the equation
5x+%2B+3y+=+54 --- (1)
Sensor B uses 4 gm zinc, 5 hours, costing 64. So we get the equation
4x+%2B+5y+=+64 --- (2)
To solve the two equations:
Multiply (1) by 4 to get
20x+%2B+12y+=+216 --- (3)
Multiply (2) by 5 to get
20x+%2B+25y+=+320 --- (4)
Subtracting (3) from (4) to eliminate x
20x+-+20x+%2B+25y+-+12y+=+320+-+216 or
13y+=+104 or y+=+104%2F13+=+8
Substituting for y in (2) we get
4x+%2B+5%2A8+=+64 or 4x+=+64+-+40+=+24
i.e. x+=+6
Cost of zinc = $6 per gram
Labour charge = $8 per hour
Check
Sensor A uses 5 gm zinc, 3 hours, cost is
6 * 5 + 8 * 3 = 30 + 24 = 54. Check correct!
Sensor B uses 4 gm zinc, 5 hours, cost is
6 * 4 + 5 * 8 = 24 + 40 = 64. Double check!
Ans: zinc cost = $6, labour cost = $8