Suppose y varies directly with x, and y = 24 when x = 8. What is the value of y when x = 10?
(1 point)
Responses
10
10
30
30
80
80
240
The correct answer is 30.
Since y varies directly with x, it means that the ratio between y and x is constant. In other words, you can find this constant ratio by dividing the given values for y and x.
So, the constant ratio (k) can be found as:
k = y/x = 24/8 = 3
Now, using this constant ratio, we can find the value of y when x = 10:
y = k * x = 3 * 10 = 30
So, y = 30 when x = 10.
To find the value of y when x = 10, we can use the concept of direct variation.
Direct variation means that y is directly proportional to x, so we can write the equation as y = kx, where k is the constant of variation.
We are given that y = 24 when x = 8. Plugging these values into the equation, we get:
24 = k * 8
To find the value of k, we divide both sides of the equation by 8:
k = 24 / 8
k = 3
Now that we have the value of k, we can substitute it back into the equation to find the value of y when x = 10:
y = 3 * 10
y = 30
So, the value of y when x = 10 is 30.