In planning for a new item, a manufacturer assumes thatthe number of items produced x and the cost in dollars C of producing these itemsare related by a linear equation. Projections are that 100 items will cost $10,000 toproduce and that 300 items will cost $22,000 to produce. Find the equation thatrelates C and x.
Those of you who help me, I really appreciate your time. I was not blessed with math ability like you, be thankful you have it.
2006-08-09 05:36:21 · 2 answers · asked by sistermoon 4 in Education & Reference ➔ Homework Help
The first situation is C = 100x
The second is C = 73 1/3 x
2006-08-09 06:06:39 · answer #1 · answered by MollyMAM 6 · 0⤊ 0⤋
The point is that there is ONLY ONE equation that can describe both situations.
Start with C=sx+y; you need to find the values of s and y to complete the problem.
Substitute the values you were given for C and x:
10000 = 100s+y
22000 = 300s+y
Multiply the ENTIRE bottom equation by -1 and then add the two equations together:
10000 = 100s+y
-22000 = -300s-y
The result is:
-12000 = -200s
Therefore, after dividing both sides of the equation by -200 you get:
s=600.
Now that you know s, you can use either of your two original equations to solve for y (I used the first):
10000 = 60 (100) + y
Therefore y = 4000.
Your final solution is C = 60x + 4000.
2006-08-09 13:11:02 · answer #2 · answered by Anonymous · 0⤊ 0⤋