How to solve this???

Question

A company manufactures small refrigerators. The total cost to manufacture 42 refrigerators is $4520. The total costs to manufacture 107 refrigerators is $10695. Assume that total cost, C, is linearly related to the number of refrigerators, x, the company manufactures and includes a fixed cost and a cost per refrigerator.

A) Write the cost function, C(x)C(x) in terms of x, the number of refrigerators manufactured. 

Answer 1

(42, 4520) and (107, 10695)

(10695 -4520)/(107-42)

= 6175/65

= 1235/13

= 95 = (y-4520)/(x-42)

y-4520 = 95(x-42)

y = 95x -42(95)- + 4520

y = 95x --3990 +4520

y = 95x+ 530

Answer 2

We will set this up as a linear equation with x as the number of refrigerators and C as the cost to manufacture x refrigerators.

We have the points (42,4520) and (107, 10695). First find the slope which is (10695 - 4520)/(107 - 42) = 6175/65 = 95.

This is the fixed cost which is $95 for each additional refrigerator.

Now to find the fixed cost we use one of the points. 4520 = 95(42) + b

From this b = $530

We check with the other point

10695 =? 95(107) + 530

It checks so our equation is C(x) = 95x + 530