If x and y vary directly, and x = 12 when y = 3, what will be the value of x when y = 9?

Direct proportion is the relationship between two variables whose ratio is equal to a constant value.

Answer: If x and y vary directly, and x = 12 when y = 3, then the value of x when y = 9, is equal to 36.

Let's look into the relationship between x and y.

Explanation:

Given: x = 12, y = 3

Since, x is directly proportional to y we have,

x ∝ y

=> x = ky           (where, k = constant of proportionality)

=> x/y = k ----------------------- (1)

By substituting the values of x and y in equation (1) we get,

k = 12/3 = 4

Thus, x/y = 4         (from equation (1))

Now, y = 9, x = ?

x = ky

=> x = 4 × 9           (since, k = 4)

=> x = 36

Thus, if x and y vary directly, and x = 12 when y = 3, then the value of x when y = 9, is equal to 36