Question

The variable y varies directly as x. When x = 20, y = 12. What is the value of y when x = 15?

A) 7
B) 9
C) 18
D) 25

Answer 1

To find the value of y when x = 15, we first determine the constant of variation k from the given values (x = 20, y = 12). We then use k to calculate the new value of y for x = 15, which yields y = 9.

Step-by-step explanation:

The student's question is about direct variation and how to find the value of y for a given value of x when there is a known relationship between x and y. In this case, we are given that y varies directly as x and that when x = 20, y = 12. This allows us to find the constant of variation, k, since y = kx. We calculate k as:

y = kx
12 = k * 20
k = 12 / 20
k = 0.6

Now, with k known, we can find the value of y when x = 15:

y = kx
y = 0.6 * 15
y = 9

Therefore, when x = 15, the value of y is 9, which corresponds to option B).