Final answer:
To solve the problem, set up a proportion to find the total number of pencils that will fit into Rana's pencil box. The answer is 24 pencils.
Step-by-step explanation:
To solve this problem, we can set up a proportion to find the total number of pencils that will fit into Rana's pencil box. Let x represent the total number of pencils. We know that the box is initially half full, which is represented by x/2. After Rana puts four extra pencils in, the box is now two-thirds full, or 2x/3. We can set up the proportion: x/2 = 2x/3. To solve for x, we can cross-multiply and solve the resulting equation: 3x = 4(2x). Simplifying, we get 3x = 8x. Dividing both sides of the equation by 8, we get x = 24. Therefore, the pencil box can hold 24 pencils.