1. **State the problem:** We have a box with 40 marbles. The ratio of red marbles to total marbles is $2:5$, and the ratio of green stones to total stones is $3:10$. We want to find how many stones are blue, where blue stones are those that are neither red nor green. 2. **Analyze the given ratios:** - Red marbles to total marbles ratio is $\frac{2}{5}$. - Green stones to total stones ratio is $\frac{3}{10}$. 3. **Calculate the number of red marbles:** Since there are 40 marbles total, the number of red marbles is: $$\text{Red marbles} = \frac{2}{5} \times 40 = 16$$ 4. **Calculate the total number of stones:** The problem states "stones" and "marbles" separately, but since the box contains marbles and stones, and the total marbles are 40, we need to find the total stones. However, the problem does not give the total number of stones explicitly. We assume the total stones are the same as total marbles (40) because the ratios are given relative to total stones and total marbles respectively. 5. **Calculate the number of green stones:** Using the ratio $\frac{3}{10}$ for green stones to total stones: $$\text{Green stones} = \frac{3}{10} \times 40 = 12$$ 6. **Calculate the number of blue stones:** Blue stones are those that are neither red nor green. Total stones = 40, so: $$\text{Blue stones} = 40 - (\text{Red marbles} + \text{Green stones}) = 40 - (16 + 12) = 12$$ **Final answer:** There are **12 blue stones** in the box.