In a bag, red and blue marbles are in the ratio 2 : 3. If there are 12 red marbles, how many blue marbles are there and how many marbles are there in total?

Step 1: Represent the ratio

The problem states that the ratio of red marbles to blue marbles is $2:3$. We can represent the number of red marbles as $2x$ and the number of blue marbles as $3x$, where $x$ is a common multiplier.

Step 2: Find the value of x

We are given that there are 12 red marbles. Since we represented the number of red marbles as $2x$, we can set up the equation $2x = 12$. Solving for $x$ gives us the value of the common multiplier.

Step 3: Calculate the number of blue marbles

Now that we have found the value of $x$, we can calculate the number of blue marbles by substituting $x=6$ into our expression for blue marbles, which is $3x$.

Step 4: Calculate the total number of marbles

To find the total number of marbles, we simply add the number of red marbles and the number of blue marbles together.

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