Questions: 12 red marbles; 4:3

Solution Steps

To solve this problem, we need to determine the number of blue marbles given the ratio of red to blue marbles is 4:3 and there are 12 red marbles. We can set up a proportion based on the given ratio and solve for the number of blue marbles.

We are given that the ratio of red marbles to blue marbles is \( \frac{4}{3} \). This means for every 4 red marbles, there are 3 blue marbles.

Let \( r \) be the number of red marbles and \( b \) be the number of blue marbles. From the ratio, we can express this as: \[ \frac{r}{b} = \frac{4}{3} \] Given that \( r = 12 \), we can substitute this value into the equation: \[ \frac{12}{b} = \frac{4}{3} \]

To find \( b \), we can cross-multiply: \[ 12 \cdot 3 = 4 \cdot b \] This simplifies to: \[ 36 = 4b \] Dividing both sides by 4 gives: \[ b = \frac{36}{4} = 9 \]

Final Answer