Final answer:
The value of y, when x is 3 1/4, is found by first determining the constant of variation from the given values (y = 35 when x = 2 1/2), and then using this constant to find the new value of y. With the constant established as 14, the value of y is calculated to be 45 1/2 for x equal to 3 1/4.
Step-by-step explanation:
To solve the problem, we need to establish the relationship between x and y when they vary directly. This means as x increases, y increases at the same rate and vice versa, described by the equation y = kx where k is the constant of variation.
We're given that when y = 35, x = 2 1/2. First, we convert 2 1/2 to an improper fraction: 2 1/2 = 5/2. We use these values to find k:
35 = k * (5/2)
Multiplying both sides by 2/5 gives us k = 14.
Now we can find the value of y when x is 3 1/4. Again, we convert 3 1/4 to an improper fraction: 3 1/4 = 13/4. Substituting k and x into the original equation yields:
y = 14 * (13/4)
By multiplying these, we get y = 91/2 or 45 1/2, which is answer choice D.