How many blue marbles in the bag?

Question

A bag contains red and blue marbles. In a representative sample of

10

​marbles, there are

5

blue

marbles. If the bag has

200

​marbles, estimate the number of

blue

marbles and

red

marbles in the bag.

Answer 1

In the representative sample there are 5 blue out of 10 total marbles:

blue / total = 5 / 10

So, if the bag contains a total of 200 marbles we can estimate the number of blue marbles:

5 / 10 = x / 200

x = 5 * 200 / 10

x = 100 blue marbles

If in a total of 200, there are 100 blue. Then, there are 200-100 = 100 red marbles.

Estimated 100 blue marbles and 100 red marbles.

Answer 2

Here's what we know:

1. The sample bag has 10 marbles.
2. The bag is made up of blue and red marbles.
3. 5 of them are blue.
4. This leads us to determine that when we subtract the 5 blue marbles from the bag, then we are left with 5 marbles that are red. 10-5=5 or 5+5=10

Here's what we want to know:

1. How many blue marbles and red marbles can we estimate there are in a bag of 200 marbles?

We use the sample bag of 10 marbles to help us with our estimation.

So if we compare the two bags, we see the following:

Sample Bag1 %

5 blue ? blue 50% blue

5 red ? red 50% red

10 total 200 total 100% total

We see that half the sample bag is blue, half the bag is red; 50% blue, 50% red. Therefore, we can reasonably estimate that there are 100 blue marbles in the bag and 100 red marbles in the bag. 100 is half of 200 OR 50% (100/200 = 1/2)