I'm great at math and I do all of these in my head. It's easy,
say it's asking for chickens and 3l-cows. You just take the number of heads, multiply it by 2, pretend all the heads are chickens, this is your base number as it caNOT be less than this right? Then take the number you get and subtract it from the number of actual legs. now since those cows have one more leg than a chicken, for each chicken you replace you get one more leg. When you subtracted you actually found HOW many cows there are, or HOW many chickens you must replace to equal that many legs! Now if the question is asking for the # of chickens, remember you are REPLACING these chickens with cows so you need to subtract the number of cows from the MAXIMUM number of chickens (or the number of heads).
As a simpler formula it would be (H)eads (x) 2 = (B)ase, (L)egs (-) (B)ase = (3l) cows, (H)eads (-) (3l) cows = (C)hickens
say it's asking for 3l-cows and (4 legged) horses? You'd do the same thing, except replace the (2 legged) chickens with 3l-cows and the cows with horses. remember to multiply the heads by 3 and go from there.
Formula: (H)eads (x) 3 = (B)ase, (L)egs (-) (B)ase = (Ho)rses, (H)eads (-) (Ho)rses = (3l) cows
say it's asking for chickens and horses?? DON'T PANIC! It's pretty much the same. Multiply the heads by 2 then subtract your sum (total) from the legs. only difference is horses have 2x as many legs as chickens. so to take that into account you'd have to add by 2 every time you replaced a chick with a horse. Well to save some time simply take your answer from the subtraction question, that difference (answer) represents how many you'd need to replace if your horses had one more leg than a chicken. Here's the catch, horses have 2 more legs than a chicken which is 2 (x) the 1
SO you need to divide your difference (answer) by 2! the answer to THAT one (quotient) would be your amount of horses. if you need the amount of chickens subtract horses from heads
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Formula: (H)eads (x) 2 = (B)ase, (L)egs (-) (B)ase = (N)oonan (/ <--- there is no divided by symbol here
) 2 = (Ho)rses, (H)eads (-) (Ho)rses = (C)hickens
My only problem is I play a lot when I just get home from work :/ and am tired lol... so I tend to make mistakes