Final answer:
To solve this problem, set up a system of equations using the given information. Solve the equations to find the number of sheep on the farm.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's say the number of sheep is represented by x and the number of cows is represented by y. We know that the ratio of sheep to cows is 3:5, so we can write the equation x/y = 3/5. We also know that there are 26 more cows than sheep, so we can write another equation as y = x + 26.
Now, we can solve these equations simultaneously to find the number of sheep on the farm. First, let's solve the second equation for x: x = y - 26. Next, substitute this expression for x in the first equation: (y - 26) / y = 3/5. Now we can cross multiply and solve for y: 5(y - 26) = 3y. Simplifying this equation gives us 5y - 130 = 3y. Combining like terms gives us 2y = 130, and dividing both sides by 2 gives us y = 65.
So there are 65 cows on the farm. To find the number of sheep, substitute this value of y back into the second equation: x = 65 - 26 = 39. Therefore, there are 39 sheep on the farm.