The number of cattle on a ranch was four times the number of horses. After 280 cattle were sold, there were twice as many horses as cattle. What were the total numbers of horses and cattle on the ranch before the 280 were sold?
c = 4 h
2 (c - 280) = h
c = 8 (c - 280)
solve for c, then substitute back to find h
280
To solve this problem, we'll use algebra to represent the relationships between the number of cattle and horses on the ranch.
Let's assume the number of horses on the ranch is "x." Since the number of cattle is four times the number of horses, we can say the number of cattle is 4x.
According to the problem, after 280 cattle were sold, there were twice as many horses as cattle. So, the number of horses after the sale would be 2 times the number of cattle remaining, which is 4x - 280.
Now, we can set up an equation to find the value of x:
4x - 280 = 2(4x)
First, let's distribute 2 to 4x: 4x - 280 = 8x
Next, let's simplify the equation by moving the variables to one side: 280 = 4x
Now, divide both sides of the equation by 4: x = 70
This tells us that the number of horses on the ranch before the cattle were sold is 70.
To find the number of cattle, we can substitute the value of x back into our expression: 4x = 4 * 70 = 280
Therefore, the number of cattle on the ranch before the sale was 280.
In conclusion, there were 280 cattle and 70 horses on the ranch before the 280 cattle were sold.