Question

75% of the marbles in a bag are orange and the rest are blue. What fraction of the orange marbles must be removed from the bag so that 50% of the remaining marbles are orange?

Answer 1

To make 50% of the remaining marbles orange after initially having 75% orange, you would need to remove 2/3 of the orange marbles.

Step-by-step explanation:

Let's assume there are 100 marbles in the bag to make the calculations easier since percentages are given. Initially, 75% of the marbles are orange, which means we have 75 orange marbles and 25 blue marbles. We want to find out how many orange marbles must be removed so that, of the remaining marbles in the bag, 50% are orange.

To end with 50% orange marbles, the number of orange and blue marbles must be equal. Since we are not removing any blue marbles and only removing orange marbles to reach this equal number, the blue marbles define our target number. We started with 25 blue marbles, thus we will need to have 25 orange marbles left.

To reach 25 orange marbles from 75 orange marbles, we must remove 75 - 25 = 50 orange marbles. Therefore, we remove 50 orange marbles so that 50% of the remaining marbles are orange.

Here is the arithmetic to find the fraction of orange marbles removed: We remove 50 out of the original 75 orange marbles, so the fraction is 50/75 which simplifies to 2/3.

Answer 2

1/2

Step-by-step explanation:

75% of the marbles in a bag are orange and the rest are blue. The percentage for blue will be:

= 100% - 75%

= 25%

The fraction of the orange marbles that must be removed from the bag so that 50% of the remaining marbles are orange will be:

= 75% - 25%

= 50%

= 1/2