The Turkeys

Let T=Turkey and C=Cow. We get Eq.1 to be T+C=17; Eq.2 to be 2T+4C=56 (since turkeys have 2 feet, cows have 4). Solving 2 equations with 2 unknowns, we get 6 turkeys and 11 cows.

Solution through logical reasoning:

Assume all animals has 2 feet. So 17 animals has 34 feet. But there are 56. Thus the remaining 22 feet has to be of the cows (remaining 2 feet per cow). i.e., no. of cows = 11, no. of turkeys = 17 - 11 = 6

I'll explain Pardz Ectin solution: "Let T=Turkey and C=Cow. We get Eq.1 to be T+C=17; Eq.2 to be 2T+4C=56 (since turkeys have 2 feet, cows have 4)." From: T+C=17 we can get C=17-T, replacing in 2T+4C we get 2T+4(17-T)=56, then 2T+68-4T=56, so 68-56=4T-2T, finally 12=2T, this means that T=6

1Cow=2 Turkeys from the number of the feet point of view

Now divide the 56 feet by the 4 legs of the cow=14 cow

But you 17 animal

That means you need 3 more animals but without increasing he number of feet

So remove 3 cows from the 14 and replace them by 6 turkeys and now you have your 17 animals with their 56 feet

Started off with these two equations: 2x +4y =56, also x + y = 17. The latter transforms easily into this: 17-y = x. I substituted (17 - y) for x in the first equation, and ended up with this, 2(17-y) + 4y = 56. From there it was pretty easy to get to 2y=22, y = 11, and x=6.

With 56 feet, you'll have 28 turkeys. But there is only 17 animals, so you'll need 11 cows to fill the lack of feet (28-17=11). 11 cows have 44 feet, so 56-44=12 feet left. Therefore, Roland has 6 turkeys. P/s: My solution is what I thought, if there is any problem, please correct it for me. Thanks!

First you choose variables: the obvious choice being C for Cow and T for Turkey. C corresponds with the quantity of cows, and T corresponds to the quantity of turkeys. Next, you use these variables to set up equations that reflect the rules described in the problem. Since all of the animals are either cows or turkeys, the total sum of the animals can be represented by the equation # of Cows + # of Turkeys = 17 Total Animals or simply C+T=17. Next we look at the total feet, using the prior knowledge that (most) cows have four feet and (most) turkeys have two feet. The total feet can be made into an equation like this: 4 Feet/Cow * # of Cows + 2 Feet/Turkey * # of Turkeys = 56 Total Feet or simply 4C+2T=56. From here, we have a few options for how to do the algebra, but given that the answer is just the T value and not both values, it is desirable to directly find the T value. To eliminate the C value and solve for T, we can first solve for C in the "total animals" equation to find C=17-T. Knowing that to be true in both equations, we can substitute (17-T) for C in the "total feet" equation and get 4(17-T)+2T=56. Simplify and solve by distributing (68-4T+2T=56), combining like terms (68-2T=56) and doing a two-step solution (-2T=-12; T=6).