SOLUTION: Can someone please help me solve this word problem. In planning for a new item, a manufactures assumes that the number of items produced x and the cost of dollars C of producting

Question 92091: Can someone please help me solve this word problem.
In planning for a new item, a manufactures assumes that the number of items produced x and the cost of dollars C of producting these items are related by a linear equation. Projections are that 100 items will cost $10,000 to produce and that 300 items will cost $22,000. Find equation that relates to C and x.
Thank you.
Answer by mathispowerful(115) (Show Source): You can put this solution on YOUR website!

Assume the linear equation is
c = ax +b
then using given information we get
10000 = 100a + b
22000 = 300a + b
solve this system:
using second equation minus the first one: 200a = 12000
so a = 60
From the first equation: b = 10000-100a
= 10000 - 6000 = 4000
so we know a=60, b = 4000
the linear equation is
c = 60x + 4000
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