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