Suppose y varies directly with x, and y = 25 when x = 140. What is the value of x when y = 36?
(1 point)
Responses
140
140
165
165
201.6
201.6
176Suppose y varies directly with x, and y = 25 when x = 140. What is the value of x when y = 36?
(1 point)
Responses
140
140
165
165
201.6
201.6
176
To find the value of x when y = 36, we can use the equation for direct variation: y = kx, where k is the constant of variation.
We are given that y = 25 when x = 140.
To find k, we can use this information: 25 = k(140).
Dividing both sides of the equation by 140, we find:
k = 25/140 = 5/28.
Now we can substitute this value of k into the equation y = kx to find the value of x when y = 36:
36 = (5/28)x.
To solve for x, we can multiply both sides of the equation by 28/5:
x = (36)(28/5) = 201.6.
Therefore, the value of x when y = 36 is 201.6.
To find the value of x when y = 36, we can use the concept of direct variation.
First, let's set up the direct variation equation:
y = kx
where k is the constant of variation.
We know that y = 25 when x = 140.
Plugging these values into the equation, we get:
25 = k * 140
To find the value of k, we divide both sides of the equation by 140:
k = 25 / 140
k ≈ 0.1786
Now we can use the value of k to find the value of x when y = 36.
Plugging y = 36 and k = 0.1786 into the direct variation equation, we get:
36 = 0.1786 * x
To solve for x, divide both sides of the equation by 0.1786:
x = 36 / 0.1786
x ≈ 201.6
Therefore, when y = 36, the value of x is approximately 201.6.