Here's how I solved it mathematically: Farmer 1 has 10 chickens. Farmer 2 has 16 chickens. Farmer 3 has 26 chickens. Price before lunch: x Price aft

Here's how I solved it mathematically: Farmer 1 has 10 chickens. Farmer 2 has 16 chickens. Farmer 3 has 26 chickens. Price before lunch: x Price after lunch: y # of chickens sold before lunch by farmers 1, 2, 3: a, b, c Total earned by each farmer: $35 We're told that, x > y and can logically deduce that, a > b > c because otherwise, the farmers with less chickens would have no chance of making the same amount as the other farmer.* From this information, we know that: ax + (10 - a)y = bx + (16 - b)y = cx + (26 - c)y = 35 Let's isolate the first and second farmers here: ax + (10 - a)y = bx + (16 - b)y ax - ay + 10y + bx - by + 16y = 0 (a - b)(x - y) = 6y We can do the same between farmers 1 and 3: (a - c)(x - y) = 16y These two formulas yield, (a - b) = (3 / 8)(a - c) Since a > b > c, (a - b) > 0 (a - c) > 0 Since farmer 1 only has 10 chickens, a ≤ 10 Since you can't sell negative chickens, b ≥ 0 c ≥ 0 And since the problem isn't very interesting if the farmers are allowed to sell half-chickens, a, b, and c (and the difference between them) are integers. Given all of this, 0 ≤ (a - b), (a - c) ≤ 10. The only numbers that satisfy this and, (a - b) = (3 / 8)(a - c) are, (a - b) = 3 (a - c) = 8 Since c ≥ 0 and a ≤ 10, we have three triplets to consider: a = 10: {10, 7, 1} a = 9: {9, 6, 1} a = 8: {8, 5, 0} We can find the relationship between x and y from an earlier equation: (a - b)(x - y) = 6y 3(x - y) = 6y 3x = 9y x = 3y So the farmers reduced their price to a third of the original price during the afternoon. What a deal! We've got a few equations that look like, ax + (10 - a)y = 35 Which we can now simplify to, 2ay + 10y = 35 By plugging [10, 9, 8] into the above formula, the only value that gives us a proper dollar amount for y is a = 9. So... y = $1.25 x = $4.25 Reading through the G+ comments it looks like someone beat me to it, but I figured I'd share my solution anyway. *This is assuming that they didn't decide to "sell" their chickens for $0 in the afternoon, which is probably a safe bet. Edit: add intermediate steps for clarity