There is an animal farm where chickens and cows live. All together,there are 103 heads and 278 legs. How many chickens and cows are there on the farm? square chickens and square cows Question Help: Video

This is a classic problem of system of linear equations. We can set up two equations based on the information given in the problem. Let's denote the number of chickens as C and the number of cows as W. <br /><br />From the problem, we know that:<br />1. The total number of heads (chickens and cows) is 103. This gives us our first equation: C + W = 103.<br />2. The total number of legs (chickens and cows) is 278. Since chickens have 2 legs and cows have 4 legs, this gives us our second equation: 2C + 4W = 278.<br /><br />We can solve this system of equations by substitution or elimination. Here, we'll use the substitution method.<br /><br />First, let's solve the first equation for C: C = 103 - W.<br /><br />Next, we substitute C in the second equation: 2(103 - W) + 4W = 278. Simplifying this gives: 206 - 2W + 4W = 278, which simplifies further to: 2W = 72. Solving for W gives: W = 36.<br /><br />Finally, we substitute W = 36 into the first equation to find C: C = 103 - 36 = 67.<br /><br />So, there are 67 chickens and 36 cows on the farm.