the value of y varies directly with x if x=15 when y = 195 what is the value of x when y = 39?
y = kx, so y/x = k, is constant
You want x such that
39/x = 195/15
x = 3
To find the value of x when y = 39, we can set up a proportion based on the direct variation relationship:
x1/y1 = x2/y2
Substituting the given values:
15/195 = x2/39
Now, we can cross multiply and solve for x2:
15 * 39 = 195 * x2
585 = 195 * x2
Divide both sides by 195 to solve for x2:
x2 = 585 / 195
x2 = 3
Therefore, when y = 39, the value of x is 3.
To solve this problem, we need to use the concept of direct variation. In direct variation, if two variables (in this case, x and y) are directly proportional, their ratio remains constant.
We can write the equation for direct variation as:
y = kx
Where "k" is the constant of variation.
To find the value of "k" in this problem, we can use the given information. We know that when x = 15, y = 195. So, we can substitute these values into the equation:
195 = k * 15
To find the value of "k," we divide both sides of the equation by 15:
k = 195 / 15
k = 13
Now that we know the value of "k" is 13, we can use this value to find the value of x when y = 39. Let's substitute the known values into the equation:
39 = 13 * x
To solve for "x," divide both sides of the equation by 13:
x = 39 / 13
x = 3
Therefore, when y = 39, the value of x is 3.