3. There are some red and blue marbles in a box. We are told that there are twelve more red marbles than blue marbles, and we experimentally determine that when we pick a marble randomly we get a blue marble one quarter of the time. How many marbles are there in the box?
Solution: Call the number of blue marbles $x$, so the number of red marbles is $x+12$ and the total number of marbles is $2 x+12$. The probability of picking a red marble is $\frac{x}{2 x+12}=\frac{1}{4} \Rightarrow x=6$, so $2 x+12=24$.