Variable y varies directly with variable x, and y = 4 when x = 7.

What is the value of x when y = 12?

This isn't a quiz, but I want to know concept. The answer was 21, although I'm lost in how you get it.

Question

Variable y varies directly with variable x, and y = 4 when x = 7.  
 
What is the value of x when y = 12?

This isn't a quiz, but I want to know concept. The answer was 21, although I'm lost in how you get it.

badhi · Answer

You can create an equation for the direct proportionality as-$$y = kx$$ where $k$ = constant. Since we have introduced a new unknown constant we should first find the value of k to find the x values for each y value. For that use the given information. Once you've found the value of the k you can find any y value of given x value. 

There are more quicker ways though for these kind of applications. But this is the foundation for all of them.