Farmer brown wants to spend exactly 376 dollars on cows,pigs, and sheep and he w

Question

Farmer brown wants to spend exactly 376 dollars on cows,pigs, and sheep and he wants to buy exactly 40 of these animals. If cows are 14 dollars each , pigs are 6 dollars each and sheep are 3 dollars each . How many of each should he buy (buying at least one of each species)

Explanation / Answer

let he buys c cows, p pigs and s sheeps then 14c + 6p+ 3s = 376 and c+p+s = 40 so c < 20, p < 40 and s < 40 so 11c + 3p = 376 - 120 = 256 8c + 3(c+P) = 256 let he buy 2 cows so c+p = 240/3 = 80 so p = 78 and c = 2 so s = 10 as p > 63 not possible let he buy 5 cows, now also not possible let he buy 8 cows c=8 p = 56 still p > 40 let he buy 11 cows, p =45 still > 40 let he buy 14 cows, p = 34 but c+p > 40 so not possible let he buy 17 cows, p = 23 but then sheeps = 0, not possible let he buys 20 cows, p = 12 and s = 8 so 20 cows, 12 pigs and 8 sheeps he buys

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