If y varies directly with x, and y is 252 when x is 84, what is the value of y when x is 74?

To solve for the value of y when x is 74, we first need to understand the concept of direct variation. When we say that y varies directly with x, it means that there is a constant ratio between y and x. This relationship can be expressed mathematically as:

y = kx

where k is the constant of variation.

Given that y = 252 when x = 84, we can use this information to find the value of k:

252 = k * 84

To find k, we can rearrange the equation:

k = 252 / 84

Calculating this gives us:

k = 3

Now that we have the value of k, we can express the relationship between y and x as:

y = 3x

Next, to find the value of y when x = 74, we can substitute 74 into the equation:

y = 3 * 74

Calculating this gives us:

y = 222

Therefore, the value of y when x is 74 is 222.