I am Getting Conflicting answers, Can anyone Get this Problem? Please

So its a word problem, but its an image problem: http://i.imgur.com/FvpLp.jpg And the answer is a dollar amount...

Thanks

(59.47 - 39.32) / (29 - 16) =
20.15 / 13 =
1.55

So for each increase of 1 HCF from the starting point 16 HCF, the cost increases by $1.55 from the starting point of $39.32.

$39.32 + (28 - 16) * $1.55 = $39.32 + 12 * $1.55 = $39.32 + $18.60 = $57.92

Answer: $57.92

Create the function from the two points you've been given:

16 hundred cubic feet costs $39.32

29 hundred cubic feet costs $59.47

The x (cubic feet) increases by 29 - 16 or 13 HCF.

The y (cost) increases by $59.47 - $39.32 or $20.15.

That's a slope of $20.15 / 13 or $1.55 per HCF

That makes the partial equation:

C = 1.55x + b

To solve for b, substitute either point's x and y values:

59.47 = 1.55(29) + b

59.47 = 44.95 + b

b = 59.47 - 44/95 = 14.52 (there's a minimum charge of $14.92)

The full equation is:

C = 1.55x + 14.92

Substitute 28 for x:

C = 1.55(28) + 14.92

C = 43.40 + 14.92 = $58.32

Note: The reason for the different answers is probably that the $1.55 per HCF cost leads people to think that they can use this method:

Reduce the $59.47 cost for 29 HCF by $1.55 to get a cost of $57.92.(WRONG)

The $14.92 minimum charge is still there. You need to use the full equation to get the cost right.

You're probably supposed to actually work out the slope-intercept form of the line, given that it goes from (16, 39.32) to (29, 59.47). But if I ran into this problem in real life, I'd just use linear interpolation. Here's how that works.

The value 28 is (28 - 16)/(29 - 16) = 12/13 of the way from 16 to 29.

So the cost is 12/13 of the way from $39.32 to $59.47. Take the difference ($59.47 - $39.32), multiply it by 12/13, and add to $39.32.