y varies directly with x. When y = 20, x = 50. Find x when y = 36.
y varies directly with x ----> y = kx , where k is a constant
20 = k(50
k = 2/5
y = (2/5)x
when y = 36
36 = (2/5)x
2x = 180
x = 90
or ... use a proportion
x/50 = 36/20
x = 50(36)/20 = 90
Answers
To solve this problem, we need to use the concept of direct variation. In direct variation, two variables are related in such a way that when one variable increases or decreases, the other variable also increases or decreases proportionally.
In this case, we are given that y varies directly with x, which can be written as:
y = kx
where k is the constant of variation.
We are also given that when y = 20, x = 50. Using this information, we can find the value of k:
20 = k * 50
k = 20/50
k = 2/5
Now that we have the value of k, we can substitute it back into the equation to find the value of x when y = 36:
36 = (2/5) * x
To solve for x, we can multiply both sides of the equation by 5/2:
36 * (5/2) = (2/5) * x * (5/2)
90 = x
Therefore, when y = 36, x = 90.