Suppose y varies directly with x, and y=24 when x =8. what is the value of y when x=10.
I learned how to do these kind of problems recently, but forget how to do them, and am currently unable to review the livelesson, so could someone plz help meh?
y varies directly with x means:
y = k ∙ x
if x = 8 and y = 24 then:
24 = k ∙ 8
Divide both sides by 8
3 = k
k = 3
y = 3 ∙ x
when x = 10 then:
y = 3 ∙ 10 = 30
Thank you a bunch, i got it now, thanks
Thank you so much Bosnian!
Sure! To solve this problem, we need to use the concept of direct variation. In direct variation, two variables, y and x, are related in such a way that as one variable increases or decreases, the other variable also increases or decreases proportionally.
The equation for direct variation is usually written as y = kx, where k is the constant of variation. In this case, the problem tells us that y varies directly with x. So we can write the equation as y = kx.
To find the value of k, the constant of variation, we can plug in the given values into the equation. We are told that when x = 8, y = 24. So we substitute these values into the equation:
24 = k * 8
Now we can solve for k. Divide both sides of the equation by 8:
k = 24/8 = 3
So we have found that the constant of variation, k, is 3.
Now that we know the value of k, we can use it to find the value of y when x = 10. We substitute the values into the equation again:
y = 3 * 10 = 30
So when x = 10, y is equal to 30.
Therefore, the value of y when x = 10 is 30.