To solve this problem, we need to understand the concept of direct variation. When we say that y varies directly with x, it means that there is a constant ratio between y and x. We can express this relationship with the equation:
y = kx
Here, k is the constant of variation. From the information provided, we know:
- x = 75 when y = 10
First, we can find the value of k by substituting these values into the equation:
10 = k * 75
To solve for k, we divide both sides by 75:
k = 10 / 75
Now, simplifying that:
k = 2 / 15
Now that we have the value of k, we can use it to find the value of x when y = 4:
Substituting into the direct variation equation:
4 = (2 / 15) * x
To find x, we can multiply both sides by the reciprocal of (2/15), which is (15/2):
x = 4 * (15 / 2)
Calculating that:
x = 60
So when y is 4, the corresponding value of x is 60. Therefore, in summary, the answer is:
x = 60