suppose y varies directly with x, and y = 25 when x = 140. What is the value if y when x = 36?
a.) 140
b.) 165
c.) 201.6
d.) 176
To find the value of y when x = 36, we can use the concept of direct variation. Direct variation can be represented by the equation y = kx, where k is the constant of variation.
We are given that y = 25 when x = 140. We can plug these values into the equation to find the value of k.
25 = k * 140
To solve for k, divide both sides of the equation by 140:
k = 25/140
Simplifying the fraction gives:
k ≈ 0.1786
Now that we have the value of the constant of variation (k), we can find the value of y when x = 36 by plugging it into the equation:
y = (0.1786)(36)
y ≈ 6.4296
Therefore, the value of y when x = 36 is approximately 6.4296.
Since this value is not among the provided answer choices, there may be an error in the problem statement or answer choices.
To find the value of y when x = 36, we can use the direct variation formula, which relates the two variables as y = kx, where k is the constant of variation.
To determine the value of k, we can use the given information that y = 25 when x = 140. Substituting these values into the formula, we have:
25 = k * 140
Now, solve for k:
k = 25 / 140 = 0.17857142857142858
Now that we have the value of k, we can substitute it back into the direct variation formula to find y when x = 36:
y = k * x
y = 0.17857142857142858 * 36
y ≈ 6.428571428571429
Therefore, the value of y when x = 36 is approximately 6.43.
From the given options, there is no exact match for the value of 6.43. The closest option is 201.6 (c.), which is not an accurate representation of the value. Therefore, none of the provided options is the correct answer.
y=kx
k=y/x=25/140
y=kx= (25/140) x
y=(25/140) 36=25*36/140= ?