 
<translate> Da farko, za a ci ciyawa mai girman eka 144 bisa ga lissafi 5 * 2 * T + 8 * 1 * T = 144. Warware wannan daidaituwa don T, mun sami 18 * T = 144, ko T = watanni 8 na abinci an rufe da dabbobin da ke kiwo a kan makiyaya. Wannan yana nufin manomi dole ne ya sayi hatsi mai shayarwa don sauran watanni 12 - 8 = 4. Bayan haka, tumakin makiyayin 8 za su buƙaci 4 / 2 = 2 bags na hatsi na hatsi kowanne, ko 8 * 2 = 16 bags na hatsi na hatsi gaba ɗaya don tsawon watanni 4. Shanu 5 na rancher za su buƙaci 4 / 1 = 4 buhunan hatsi na hatsi kowanne, ko 5 * 4 = 20 buhunan hatsi na hatsi a cikin duka don watan. Saboda haka, mai gonar yana bukatar 16 + 20 = buhunan hatsi 36 don dukan dabbobinsa. Don haka, mai ranch zai bukaci ya kashe 36 * 10 = $ 360 a kowace shekara a kan abincin masara. Amsar ita ce: 360. <eng> First, the 144 acres of grass will be eaten according to the equation 5 * 2 * T + 8 * 1 * T = 144. Solving this equation for T, we find 18 * T = 144, or T = 8 months of food are covered by the animals grazing on the rancher's pasture. This means the farmer must buy feed corn for the remaining 12 - 8 = 4 months. Next, the rancher's 8 sheep will require 4 / 2 = 2 bags of feed corn each, or 8 * 2 = 16 bags of feed corn in total for the 4 month period. The rancher's 5 cows will require 4 / 1 = 4 bags of feed corn each, or 5 * 4 = 20 bags of feed corn in total for the month. Therefore, the rancher needs 16 + 20 = 36 bags of feed corn for all of his animals. So, the rancher will need to spend 36 * 10 = $360 per year on feed corn. The answer: 360. 