I am really stumped on this math problem?

A manufacturer finds that the cost C (in dollars)

of producing a new product line and the number of items,

x, produced are related by a linear equation.

Suppose that the cost of producing 50 items will be $3,750

and the cost of producing 400 items will be $12,500.

Use this information to find the cost of producing 470 items.

F + 50x = 3,750

F + 400x = 12,500

350x = 8,750

x = 25

F = 2,500

The cost of producing 470 items:

(F + 470x = 2,500 + 11,750)

= $14,250

All night for this? use the information "linear equation" It means C = ax+b for some a and b.

now use the other information.3750 = a(50) +b and 12500 = 400a + b

Subtracting we get, 350a = 8750 so a = 25 and then you can calculate b = 2500

so C = 25x+2500. now for x = 470, C = 25(470)+2500 = 14250. As simple as that.

Here we use the information . 3750 = a(50) +b and 12500 = 400a + b

Subtracting we get, 350a = 8750 so a = 25 and then you can calculate b = 2500

so C = 25x+2500. now for x = 470, C = 25(470)+2500 = 14250. As simple as that.

y = mx + c

$3,750 = 50x + c

Also

$ 12,500 = 400x + c

subtract one from the other

$12,500 - $3,750 = 400x - 50x +c - c

$8,750 = 350x

$875 = 35x

$175 = 7x

$25 = x

$3,750 = 50x + c

But x = $25

so $3,750 = 50 * $25 + c

$3,750 = $1,250 + c

$2,500 = c

So y = mx + c

y = 470*$25 + $2,500

y= $11,750 + $2,500

y = $14,250