Final answer:
To find x when y varies directly as x and y = 30, we first find the proportionality constant k using the initial condition (k = y/x). Using this constant, we solve for x with the equation x = y/k, leading to a result of x = 22.5.
Step-by-step explanation:
To solve for the variable x when y varies directly as x and given that x = 15 when y = 20, we use the proportionality constant. First, find the constant (k) by using the initial condition: k = y/x. Therefore, k = 20/15 = 4/3. Now, when y = 30, we use the same proportionality constant to find the new value of x. The equation becomes y = (4/3)x, so we can solve for x by rearranging the equation: x = y/(4/3).
Substitute the known value of y into the equation: x = 30/(4/3). Simplify this to find x = 22.5. Thus, when y = 30, the value of x is 22.5.