Given Information:
- x and y vary directly
- When x = 2, y = 76

To Find:
- Value of x when y = 57

Direct Variation:
In direct variation, two variables are related in such a way that when one variable increases or decreases, the other variable also increases or decreases by the same factor. Mathematically, it can be represented as y = kx, where k is the constant of variation.

Step 1: Find the constant of variation (k)
To find the constant of variation (k), we can use the given information. When x = 2, y = 76. Substitute these values into the equation y = kx and solve for k.

76 = 2k

Divide both sides of the equation by 2:
76/2 = k
38 = k

So, the constant of variation (k) is 38.

Step 2: Find x when y = 57
Now that we have the constant of variation (k), we can use it to find x when y = 57. Substitute the values into the equation y = kx and solve for x.

57 = 38x

Divide both sides of the equation by 38:
57/38 = x
1.5 = x

Therefore, when y = 57, x = 1.5.

Summary:
- The constant of variation (k) is found to be 38 using the given information where x = 2 and y = 76.
- Using the constant of variation, we find that when y = 57, x = 1.5.