To determine the value of y when it varies directly with x, we can use the formula:
y = kx
where k is a constant. First, we need to find the value of k using the provided information. We know that when y = 52, x = 84. Substituting these values into the equation:
52 = k * 84
Now, solve for k:
k = 52 / 84
Calculating k gives:
k = 0.61905 (approximately)
Now that we have the value of k, we can find y for a new value of x. We want to find y when x = 27. Using the formula:
y = k * x
Substituting k and x into the equation:
y = 0.61905 * 27
Now, calculating y gives:
y ≈ 16.69
Thus, when x = 27, the value of y is approximately 16.69.