A measurement y varies directly with regard to another value x. If y = 9 and x = 24, find x for y = 25.
y = kx
9 = k*24
k = 3/8
y = 3/8 x
25 = 3/8 x
x = 200/3
y = kx
9 = k*24
k = 3/8
y = 3/8 x
25 = 3/8 x
x = 200/3
To solve this problem, we can set up a proportion and use the concept of direct variation to find the value of x for a given value of y.
In direct variation, two variables are directly proportional if they always have a constant ratio. This means that if y varies directly with x, we can write the relationship as:
y = kx
where k is the constant of variation. In this case, we need to determine the value of k.
Given that y = 9 when x = 24, we can substitute these values into the equation:
9 = k * 24
To solve for k, we divide both sides of the equation by 24:
k = 9 / 24
Simplifying the right side gives us:
k = 3 / 8
Now that we have the value of k, we can use it to find x when y = 25. Set up the new equation:
25 = (3/8) * x
To solve for x, multiply both sides of the equation by 8/3:
x = (25 * 8) / 3
Evaluating the right side gives us:
x = 200 / 3
So x is equal to approximately 66.67 when y = 25.