Cause its Todd Burnard birthday
8 cows (They all have 2 legs)
94 three legged cows and 25 chickens.
28
Do-it-in-your-head method: If all animals were chickens there would be 96 legs. There are 26 extra legs, each on a cow, so there are 26 cows and therefore 22 chickens.
If all animals were horses there would be 4 x 59 ie 236 legs. There is a shortage of 25 legs so there are 25 cows (and 34 horses).
Do-it-in-your-head method: If all animals were chickens there would be 90 legs. There are 20 extra legs, each on a cow, so there are 20 cows and therefore 25 chickens.
51 horses of which there are 3 cows with 2 heads and three legs or since there are no 3 legged cows there are 60 horses
Do-it-in-your-head method: If all animals were horses there would be 4 x 46 ie 184 legs. There is a shortage of 31 legs which means there are 31 cows (and 15 horses). 31 x 3 = 93, 15 x 4 = 60 total 153. Shazam!
7 cows and 11 chickens. Cows have 4 legs. Chickens have 2 legs. (4 legs)(7 cows) + (2 legs)(11 chickens) = 50 legs. 7 cow heads = 11 chicken heads = 18 heads.
You are supposed to: 1) Write two equations, one for the number of heads (express it in terms of the number of cows and horses, which of course are expressed as variables), and one for the number of legs (also expressed as an equation in terms of the number of cows and horses. 2) Solve the two equations simultaneously.
If all the animals were horses there would be 360 legs. There is a shortfall of 23 which means 23 cows and therefore 67 horses.
There are 21 three-legged cows and 27 chickens on the farm. Let us say the number of cows = A and the number of chickens is B. The equation for heads is: A+B = 48 The equation for legs is: 3A + 2B = 117 (because a cow has 3 legs and a chicken has 2 legs in this question) We can rearrange the equation for heads as follows: A+B = 48 B = 48-A Now we can replace B in the equation for legs with 48-A as follows: 3A + 2(48-A) = 117 ...and solve: 3A + 96 - 2A = 117 A + 96 = 117 A = 21 So we know there are 21 three-legged cows and from earlier, B = 48-A, so B = 48-21 = 27. Therefore there are 27 chickens.