In a box, the ratio of the number of red marbles to the number of blue marbles is 2:5. 1/3 of the red marbles are removed from the box. Find the ratio of the number of red marble to the number of blue marbles in the box in the end. Express your answer in the simplest form.
(2/3 * 2x)/(5x) = (4/3)/5 = 4/15
To find the ratio of the number of red marbles to the number of blue marbles in the box after removing 1/3 of the red marbles, we can start by assigning variables to the quantities involved.
Let's assume that the original number of red marbles is represented by the variable "r," and the original number of blue marbles is represented by the variable "b."
We are given that the ratio of red marbles to blue marbles is 2:5, which means that r/b = 2/5.
Next, we are told that 1/3 of the red marbles are removed from the box. This means that (1/3) * r red marbles were removed.
The remaining number of red marbles in the box after removal can be found by subtracting the number of red marbles removed from the original number of red marbles, which gives us r - (1/3) * r = (2/3) * r.
So now we have the new number of red marbles, (2/3) * r, and the same number of blue marbles, b.
To find the new ratio of red marbles to blue marbles, we divide the new number of red marbles by the number of blue marbles:
(2/3) * r / b.
Using the original ratio, r/b = 2/5, we can substitute r/b with 2/5:
(2/3) * (2/5) = 4/15.
Therefore, the ratio of the number of red marbles to the number of blue marbles in the box after removing 1/3 of the red marbles is 4:15.