Understanding Direct Variation
When we say that y varies directly with x, it means that the ratio of y to x remains constant. This implies that we can express this relationship as:
y = kx
where k is a constant of variation. To find the value of k, we can use the values provided:
y = 10 when x = 75
Plugging these values into our direct variation formula:
10 = k * 75
We can solve for k:
k = 10 / 75 = 2 / 15
Finding x when y is 4
Now that we have the constant k, we can use it to find x when y equals 4:
y = kx
Substituting in our values:
4 = (2 / 15)x
To solve for x, we multiply both sides by 15:
4 * 15 = 2x
This simplifies to:
60 = 2x
Now, dividing both sides by 2 gives us:
x = 30
Conclusion
In conclusion, when y is 4, the value of x is 30. Understanding direct variation helps in solving such problems effectively!