Hi, I just started learning about direct, joint, and inverse variation. I was doing a practice question and got -18 when the answer is -8. I'm having trouble solving the problem because my book only shows me how to find y not x. Please help me.
If y varies inversely as x and y=-14 when x=12, find x when y=21.
Nvm I figured it out.
we know that xy = k, a constant
So, we need x such that
21x = -14*12
x = -8
You can see how to solve it without knowing what k is. The more usual method is to do
xy = k
-14*12 = k
k = -168
So, when y=21,
21x = -168
x = -8
Too bad you didn't show your work ...
Sure, I can help you with that! The first step is to understand the concept of inverse variation. Inverse variation states that when two variables are inversely related, as one variable increases, the other variable decreases, and vice versa.
To solve the problem, we can use the inverse variation formula:
y = k/x
where y represents the dependent variable, x represents the independent variable, and k is the constant of variation.
Now, you are given that y = -14 when x = 12. Let's substitute these values into the equation:
-14 = k/12
To find the value of k, we can multiply both sides of the equation by 12:
-14 * 12 = k
-168 = k
Now, we have the value of the constant of variation, k, which is -168.
To find x when y = 21, we can substitute these values into the inverse variation equation and solve for x:
21 = -168/x
To eliminate the fraction, we can cross-multiply:
21x = -168
To solve for x, divide both sides of the equation by 21:
x = -168/21
Now, simplify the fraction:
x = -8
Therefore, when y = 21, x would be equal to -8.
I hope this explanation helps! If you have any more questions, feel free to ask.