On a farm, the ratio of cattle to sheep is 3 : 5. There are 24 more sheep than catle. How many sheep are on the farm?
5x = 3x+24
x = 12
36 cattle, 60 sheep
To find the number of sheep on the farm, we need to determine the value of the ratio between cattle and sheep. We are given that the ratio of cattle to sheep is 3 : 5.
Let's assume the number of cattle to be 3x, where x is a positive constant representing the common factor. Therefore, the number of sheep can be represented as 5x.
According to the second statement, there are 24 more sheep than cattle. So, we can create the equation:
5x = 3x + 24
To solve this equation, we simplify the equation by subtracting 3x from both sides:
5x - 3x = 24
2x = 24
Now, we can solve for x by dividing both sides of the equation by 2:
2x/2 = 24/2
x = 12
Now that we have the value of x, we can find the number of sheep by substituting the value of x back into our equation:
Number of sheep = 5x = 5 * 12 = 60
Therefore, there are 60 sheep on the farm.