Word Problem has me Baffled.....?

Question

A cattle feeder buys some feeder cattle, which average 550-lb at $115/hundred weight (that is, $115 per hundred pounds, or $1.15/lb). The price he receives when he sells them as slaughter cattle is $86/hundred weight. If he plans to make a profit of $120 per head, what will be his cost per pound for a 500-lb weight gain?

Let me know how you figure it out...I have the right answer.

Well I guess you fatten them up before you sell them.

The question is written exactly as it was in the book. The text book has the answer as 30.1 cents. ...which makes no sense to me, guess I have to ask the Prof

Answer 1

550 lb x 1.15 = 632.50 + 120.00 (profit)= 752.50

500(gain)+550=1050lbs x .86=903.00

903-752.50=150.5 <----cost per 500 lbs

$150.5/500=0.301

=30.1 Cents /lb

Answer 2

In the real world your prices are reversed.
0.86(550 + g) - xg ≥ 1.15*550 + 120
if g = 500 lb, as you imply,
0.86(1050) - 500x ≥ 1.15*550 + 120
500x ≤ - 825 - 120 + 903
500x ≤ - 42
x ≤ - $0.084
so someone must pay the feeder 8.4 cents per pound to fatten the cattle if he is to make a profit of $120 per head.

1.15(1050) - 500x ≥ 0.86*550 + 120
500x ≤ - 473 - 120 + 1,207.50
500x ≤ 614.50
x ≤ $1.229 per pound

Answer 3

how can he make a profit if the price is less when he sells them on?