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A bag contains yellow, green, blue, and white marbles. The ratio of yellow, green, blue, white marbles is $4:1:2:3$. If the bag contains $20$ marbles, then how many blue marbles are there?

 Mar 30, 2024
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Here's how to find the number of blue marbles in the bag:

Total Ratio:

We are given that the ratio of yellow, green, blue, and white marbles is 4:1:2:3. This represents the proportion of each color relative to the total number of marbles.

The sum of these ratios represents the total number of parts that make up the whole bag. In this case:

Total Ratio = 4 + 1 + 2 + 3 = 10

Fraction per Marble Color:

To find the fraction representing the proportion of each color, we can divide each value in the ratio by the total ratio:

Fraction of Yellow = 4 / 10 = 2/5

Fraction of Green = 1 / 10

Fraction of Blue = 2 / 10 (what we're solving for)

Fraction of White = 3 / 10

Total Number of Marbles:

The problem states that the bag contains 20 marbles.

Number of Blue Marbles:

Since the fraction of blue marbles (2/10) represents their proportion of the total number of marbles (20), we can set up a proportion to find the actual number of blue marbles (b):

Fraction of Blue : Total Number of Marbles = Number of Blue Marbles : Total Number of Marbles

Substituting the known values:

(2/10) : 20 = b : 20

Solving for b (Number of Blue Marbles):

Cross-multiplying:

2 * 20 = 10 * b

Divide both sides by 10:

b = 4

Therefore, there are 4 blue marbles in the bag.

 Mar 30, 2024

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