Final answer:
To find the number of marbles in the box, set up an equation using the given information. Solve this equation to find the value of x, which represents the total number of marbles in the box. The answer is 150 marbles.
Step-by-step explanation:
To find the number of marbles in the box, we need to set up an equation based on the given information. Let's assume the total number of marbles in the box is 'x'. Since the probability of choosing a red marble is one-fourth, the number of red marbles is x/4. It is given that there are 150 blue marbles, so the number of blue marbles is 150. The total number of marbles in the box is the sum of the red and blue marbles, which is x/4 + 150 = x.
We can solve this equation to find the value of x. Adding 3x/4 to both sides of the equation, we get 150 + 3x/4 = x + 3x/4. Simplifying this equation, we get 150 = 4x/4. Multiplying both sides by 4, we get 600 = 4x. Finally, dividing both sides by 4, we find that x = 150. Therefore, there are 150 marbles in the box.