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?
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Step-by-Step Solution
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.