Given three variables X, Y, and Z that satisfy the equation XY = kZ, where k is a constant, initially X is 4 and the ratio X:Y:Z is 2:3:4. If Y is changed to 12 while Z remains unchanged, what is the new value of X?

Explanation

Initially, the ratio X:Y:Z is 2:3:4 and X = 4, so Y = 6 and Z = 8. Using the equation XY = kZ, we have 4 * 6 = k * 8, which gives k = 3. When Y changes to 12 and Z stays at 8, the equation becomes X * 12 = 3 * 8. Solving for X yields X = 2.