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 solve this problem, we can set up a proportion:
Since y varies directly with x, we can write the proportion as:
y/x = k
Where k is the constant of variation.
We are given that y = 25 when x = 140. Plugging these values into the proportion, we get:
25/140 = k
Simplifying this fraction, we find that:
1/7 = k
Now, we can use this value of k to find the value of x when y = 36:
36/x = 1/7
To solve for x, we can cross-multiply:
36 * 7 = 1 * x
x = 252/1
x = 252
So, the value of x when y = 36 is 252.
To determine the value of x when y = 36, we can use the direct variation formula.
The formula for direct variation is y = kx, where k is the constant of variation.
Given that y = 25 when x = 140, we can substitute these values into the formula to find the value of k:
25 = k * 140
To solve for k, we divide both sides of the equation by 140:
k = 25 / 140
Simplifying this, we get:
k = 0.1786
Now that we have the value of k, we can use it to find the value of x when y = 36:
36 = 0.1786 * x
To solve for x, we divide both sides of the equation by 0.1786:
x = 36 / 0.1786
Calculating this, we get:
x = 201.6
Therefore, the value of x when y = 36 is 201.6.