Suppose that y varies directly with x and y=10 when x=8 what is x when y=30?
x=?
24
To find the value of x when y = 30, we need to use the given information that y varies directly with x.
We can use the formula for direct variation, which states that y = kx, where k is the constant of variation.
To find the value of k, we can substitute the given values of y and x into the equation:
10 = k * 8
To solve for k, divide both sides of the equation by 8:
k = 10/8 = 1.25
Now we have the value of k, we can use it to find the value of x when y = 30:
30 = 1.25 * x
To solve for x, divide both sides of the equation by 1.25:
x = 30/1.25 = 24
Therefore, when y = 30, x = 24.
To solve this problem, we need to use the concept of direct variation. In direct variation, two variables are directly proportional to each other, meaning that as one variable increases or decreases, the other variable also increases or decreases by the same factor.
In this case, y varies directly with x, which can be represented by the equation y = kx. Here, k is the constant of variation.
We are given that y = 10 when x = 8. To find the value of k, we can substitute these values into the equation:
10 = k * 8
Now we can solve for k:
k = 10 / 8 = 1.25
Now that we know k, we can use it to find x when y = 30. We set up the equation using the value of k:
30 = 1.25x
Now we can solve for x:
x = 30 / 1.25 = 24
Therefore, when y = 30, the value of x is 24.