A quantity, y, varies directly as x. When y = 10, x = 6.
Find x when y = 14.
4.3
8.4
23.3
60
y/x is constant, so you want x such that
14/x = 10/6
To find x when y = 14, we can use the concept of direct variation.
In a direct variation, the ratio of y to x is constant.
Using the given information, we can set up the following equation:
y = kx
Where k is the constant of variation.
We are also given that when y = 10, x = 6.
Substituting these values into the equation, we get:
10 = k * 6
Solving for k, we have:
k = 10/6 = 5/3
Now we can find x when y = 14:
14 = (5/3) * x
To isolate x, we can divide both sides of the equation by (5/3):
x = 14 / (5/3)
Simplifying this expression, we get:
x = 14 * (3/5)
x = 8.4
Therefore, x = 8.4 when y = 14.
To find the value of x when y = 14, we can use the concept of direct variation. In direct variation, two variables are related by a constant ratio. We can set up a proportion to solve for x.
First, let's write the direct variation equation: y = kx, where k is the constant of variation.
We know that when y = 10, x = 6. We can plug these values into the equation:
10 = k * 6
To solve for k, we divide both sides of the equation by 6:
k = 10/6 = 5/3
Now that we have the value of k, we can use it to find x when y = 14. Plug in these values into the direct variation equation:
14 = (5/3) * x
To solve for x, we can multiply both sides of the equation by 3/5:
x = (14 * 3/5) = 42/5 = 8.4
Therefore, x is equal to 8.4.
So, the correct option is 8.4.