You have a box that contains 200 marbles. 99% of the marbles are green, the other 1% are white.
How many green marbles would you have to remove from the box to reduce the percentage of green marbles to 98%?
Green = 0.99*200 = 198
White = 0.01*200 = 2
X green marbles removed.
(200-x) Marbles remaining.
0.98(200-x) + 2 = 200-x
196-.98x + 2 = 200-x
0.02x = 200-198 = 2
X = 100 Green marbles removed.
198-100 = 98 Green marbles remaining.
200-100 = 100 total Marbles remaining.
Check:
Green/Total = 98/100 = 0.98 = 98% Green
marbles remaining.
To determine how many green marbles would need to be removed to reduce the percentage of green marbles from 99% to 98%, we need to first find out the total number of marbles in the box after removing the desired green marbles.
Let's start by calculating the total number of green marbles in the box. Since initially 99% of the marbles are green, we can find the number of green marbles by multiplying the total number of marbles by the respective percentage:
Number of green marbles = 99/100 * 200 = 198
Next, let's determine the total number of marbles after removing x green marbles. To reduce the percentage of green marbles to 98%, we need to calculate the total number of marbles that would make up 2% of the total:
Total number of marbles = 100/2 * (Number of green marbles)/(Percentage of green marbles)
= 100/2 * 198/98
= 200
Now, let's solve for x to find the number of green marbles that would need to be removed to achieve a 98% green marble percentage:
Number of green marbles - x = 200 - x
Percentage of green marbles = (Number of green marbles - x)/Total number of marbles * 100
Setting the percentage of green marbles to 98% and substituting the known values, we can solve for x:
98 = ((Number of green marbles - x)/200) * 100
Multiplying both sides of the equation by 200 and dividing by 100 to isolate the numerator:
9800 = Number of green marbles - x
Rearranging the equation to solve for x:
x = Number of green marbles - 9800
Substituting the known value of the number of green marbles:
x = 198 - 9800
x ≈ -9602
Therefore, to achieve a 98% green marble percentage, you would need to remove approximately 9602 green marbles. However, since this result is not a positive number, it indicates that it is not possible to reduce the percentage of green marbles to 98% with the given setup.
To determine the number of green marbles you would have to remove from the box to reduce the percentage of green marbles to 98%, you need to determine the current number of green marbles and the number of marbles you need to achieve the desired percentage.
Step 1: Find the current number of green marbles.
Given that 99% of the marbles are green, you can calculate the current number of green marbles by multiplying the total number of marbles by the decimal equivalent of 99%.
Current number of green marbles = 200 * 0.99 = 198
Step 2: Calculate the desired number of green marbles.
To find the desired number of green marbles that would result in a 98% percentage, divide the desired percentage by 100 and multiply the result by the total number of marbles.
Desired number of green marbles = 200 * (98/100) = 196
Step 3: Determine the number of green marbles to remove.
The number of green marbles to remove can be found by subtracting the desired number of green marbles from the current number of green marbles.
Number of green marbles to remove = 198 - 196 = 2
Therefore, you would need to remove 2 green marbles from the box to reduce the percentage of green marbles to 98%.