SOLUTION: How would I write the linear cost function. 12 units cost $445; 50 units cost $1585. I know the answer is c(x)=3x+85 But I can't figure out how they go the 3 or the 85.

Algebra ->  Functions -> SOLUTION: How would I write the linear cost function. 12 units cost $445; 50 units cost $1585. I know the answer is c(x)=3x+85 But I can't figure out how they go the 3 or the 85.      Log On


   



Question 326064: How would I write the linear cost function.
12 units cost $445; 50 units cost $1585.
I know the answer is c(x)=3x+85
But I can't figure out how they go the 3 or the 85.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I don't know either since neither point works in the equation,
c%2812%29=3%2812%29%2B85=$121
c%2850%29=3%2850%29%2B85=$235
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The linear function would look like, y=mx%2Bb
With the first point,
1.12m%2Bb=445
With the second point,
2.50m%2Bb=1585
Subtract eq. 1 from eq. 2 to eliminate b.
50m%2Bb-12m-b=1585-445
38m=+1140
m=1140%2F38=30
Did you mean 30 instead of 3 in your solution above?
Then use either equation to solve for b.
12%2830%29%2Bb=445
360%2Bb=445
b=85
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C%28x%29=30x%2B85
Just to verify,
C%2812%29=30%2812%29%2B85=$445
C%2850%29=30%2850%29%2B85=$1585