Final answer:
To solve the problem, one must first express the number of red and blue marbles in terms of 'x' based on the given ratio. Then, by setting up an equation using the difference provided and solving for 'x', the quantity of red marbles is found by multiplying the value of 'x' by the ratio representing red marbles.
Step-by-step explanation:
The question asks to find out how many red marbles are there if the ratio of red to blue marbles is 4:7 and there are 120 more blue marbles than red marbles. We can represent the number of red marbles as 4x and the number of blue marbles as 7x. The relationship given is 7x = 4x + 120.
First, we subtract 4x from both sides to isolate the variable on one side: 7x - 4x = 120, which simplifies to 3x = 120. Next, to find the value of x, we divide both sides by 3, resulting in x = 40.
Since red marbles are represented as 4x, we multiply the value of x by 4 to find the total number of red marbles: 4 * 40 = 160. However, this is more than the options provided, indicating a possible mistake in the original question or a misunderstanding. It is important to re-evaluate the provided ratios and the difference of 120 marbles to ensure accuracy in the solution.