To find the number of red marbles given the ratio of red to blue marbles is 2:3 and there are a total of 12 marbles, you can follow these steps:
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Understand the ratio: The ratio 2:3 means for every 2 red marbles, there are 3 blue marbles. The total parts in the ratio is \(2 + 3 = 5\).
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Find the value of one part: Since there are a total of 12 marbles, you can find the value of one part by dividing the total number of marbles by the total parts in the ratio: \[ \text{Value of one part} = \frac{12 \text{ marbles}}{5 \text{ parts}} = 2.4 \text{ marbles per part} \]
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Calculate the number of red marbles: Since the ratio shows there are 2 parts of red marbles: \[ \text{Number of red marbles} = 2 \text{ parts} \times 2.4 \text{ marbles per part} = 4.8 \]
Since you cannot have a fraction of a marble, we must interpret that this is a theoretical distribution based on the ratio. To maintain whole numbers while respecting the ratio, let’s scale the total number of marbles from 12 down to the nearest workable total.
Using whole numbers in the ratio:
Since the ratio of red to blue marbles is 2:3:
- Let the number of red marbles be \(2x\)
- Let the number of blue marbles be \(3x\)
The total number of marbles is given by: \[ 2x + 3x = 12 \] \[ 5x = 12 \] \[ x = \frac{12}{5} \rightarrow 2.4 \]
Thus simplifying further to whole numbers, we can use direct multiples of the ratio: If we double the ratios for simplicity:
- Red: 4 (from the ratio 2 → multiplied by 2)
- Blue: 6 (from the ratio 3 → multiplied by 2)
So the ratio 2:3 represented in whole numbers under the constraint of 12 total marbles is indeed 4 red marbles and 6 blue marbles.
Thus, the answer is: There are 4 red marbles.