There are 10 marbles of different colours - red, blue, white in a bag. There are 5 more blue marbles than white marbles. Urmi takes 3 blue marbles. Meena takes 2 blue marbles and 1 red marble. Shanta takes 1 blue, 1 red and 1 white marble. What is the colour of the LAST marble remaining in the bag?
Well, it seems like the marbles had a colorful adventure! Let's see if we can figure out which color is the last one remaining.
Initially, we have 10 marbles in the bag. We know that there are 5 more blue marbles than white marbles, so let's assume there are x white marbles. That means there are x + 5 blue marbles.
Now Urmi takes 3 blue marbles, so we are left with (x + 5 - 3) blue marbles. Similarly, Meena takes 2 blue marbles and 1 red marble, leaving us with (x + 5 - 3 - 2 - 1) blue marbles and (1) red marble.
Finally, Shanta takes 1 blue, 1 red, and 1 white marble, which means we now have (x + 5 - 3 - 2 - 1 - 1 - 1) blue marbles, (1 - 1) red marble, and (x - 1) white marble.
Taking all this into account, we can simplify the remaining marbles as (x - 2) blue marbles, (1 - 1) red marble, and (x - 1) white marble.
Since we're looking for the color of the last marble remaining, we need to find the marble color that doesn't have any quantity left. From our simplified equation, we see that there's only one red marble remaining while the others have quantities greater than zero.
So, after this colorful adventure, the color of the last marble remaining in the bag is RED.
To find the color of the last marble remaining in the bag, let's break down the information given step-by-step:
1. The initial number of blue marbles is 5 more than the number of white marbles.
So, let's assume there are "x" white marbles. Then, the number of blue marbles is "x + 5".
2. Urmi takes 3 blue marbles.
After Urmi takes 3 blue marbles, the number of blue marbles remaining in the bag is "x + 5 - 3".
3. Meena takes 2 blue marbles and 1 red marble.
After Meena takes 2 blue marbles and 1 red marble, the number of blue marbles remaining in the bag is "x + 5 - 3 - 2", and the number of red marbles remaining is "1".
4. Shanta takes 1 blue, 1 red, and 1 white marble.
After Shanta takes 1 blue, 1 red, and 1 white marble, the number of blue marbles remaining in the bag is "x + 5 - 3 - 2 - 1", the number of red marbles remaining is "1 - 1", and the number of white marbles remaining is "x - 1".
5. As per the given information, there are 10 marbles in total.
So, the sum of all the remaining marbles should be equal to 10:
(x + 5 - 3 - 2 - 1) + (1 - 1) + (x - 1) = 10.
Simplifying the equation:
(x - 1) + x + 5 - 3 - 2 - 1 + 1 - 1 = 10
2x + x = 21
3x = 21
x = 7
Therefore, there are 7 white marbles initially.
To find the color of the last marble remaining, we need to determine the number of white marbles left after Shanta takes her turn:
Number of white marbles remaining = 7 - 1 = 6
So, the LAST marble remaining in the bag is WHITE.
To find the color of the last marble remaining in the bag, let's calculate the number of marbles of each color after each person takes their share.
Given:
- Total marbles = 10
- Colors: red, blue, white
- There are 5 more blue marbles than white marbles.
Step 1: Calculate the number of blue and white marbles.
Let's assume the number of white marbles is W. So, the number of blue marbles is W + 5.
We know that W + (W + 5) + 1 (red marble) = 10 (total marbles).
Simplifying the equation: 2W + 6 = 10
Subtracting 6 from both sides: 2W = 4
Dividing both sides by 2: W = 2
So, there are 2 white marbles and 2 + 5 = 7 blue marbles initially.
Step 2: Subtract the marbles taken by each person.
- Urmi takes 3 blue marbles: 7 blue marbles - 3 = 4 blue marbles remaining.
- Meena takes 2 blue marbles and 1 red marble: 4 blue marbles - 2 = 2 blue marbles remaining, and 1 red marble remaining.
- Shanta takes 1 blue, 1 red, and 1 white marble: 2 blue marbles - 1 = 1 blue marble remaining, 1 red marble remaining, and 2 white marbles remaining.
Step 3: Calculate the color of the last marble remaining.
We have 1 blue marble, 1 red marble, and 2 white marbles remaining.
Therefore, the color of the last marble remaining in the bag is white.
So, the answer is the last marble remaining in the bag is white.
Number of white --- x
number of bue = x+5
number of red = 10 - x - x-5 = 5 - 2x
So clearly 5 -2x > 0
x < 2.5
so x = 1 or x = 2
case 1: x = 1 --> 1 white, 6 blue, 3 red
after the grabbing of marbles:
6 blues are taken, 2 red are taken, 1 white is taken
leaving 1 red marble
case 2: x = 2, ---> 2 white, 7 blue, 1 red
but it said 2 reds are taken and we only had one red,
So case 2 is not possible
must be case 1 , see above