If (x + 3) varies directly as y and x = 3 when y = 12, what is the value of x when y = 8?
Answer Details
In a direct variation, two variables are related by a constant ratio. This can be expressed mathematically as:
x ∝ y
which means that x is directly proportional to y, or that x and y vary directly. We can also write this relationship as an equation:
x = ky
where k is the constant of proportionality.
In this problem, we are given that (x + 3) varies directly as y. So we can write:
x + 3 = ky
where k is some constant of proportionality that we don't know yet.
We are also given that x = 3 when y = 12. We can use this information to solve for k:
x + 3 = ky
3 + 3 = k(12)
6 = 12k
k = 0.5
Now that we know k, we can use the equation x + 3 = ky to find x when y = 8:
x + 3 = ky
x + 3 = 0.5(8)
x + 3 = 4
x = 1
Therefore, when y = 8, x = 1. The answer is (a) 1.