Assume y varies directly as x.
If x = 2 when y = 7, find x when y = 32.
To find the value of x when y = 32, we need to use the concept of direct variation. Direct variation states that two variables, in this case, y and x, are directly proportional to each other. Mathematically, this can be expressed as:
y = kx
where k is the constant of proportionality.
To find the value of k, we can use the initial values given in the problem. It is stated that when x = 2, y = 7. Plugging these values into the equation, we get:
7 = k(2)
To solve for k, divide both sides of the equation by 2:
k = 7/2
Now that we have the value of k, we can substitute it back into the equation to find the value of x when y = 32:
32 = (7/2)x
To solve for x, multiply both sides of the equation by 2/7:
(2/7)(32) = x
x ≈ 32/7
Therefore, when y = 32, x is approximately equal to 32/7.