Final answer:
To solve the problem, we calculate the total weight constraints imposed by the ratios and deduce the multiplier x. Applying this multiplier to the ratio that corresponds to dangerous stones, we find there are 8 dangerous stones.
Step-by-step explanation:
We are tasked with determining the number of dangerous stones, given that the ratio of marvelous stones to dangerous stones is 3:4 and the total weight is 86kg, with average weights of 5kg and 7kg respectively.
Let the number of marvelous stones be 3x and the number of dangerous stones be 4x. Multiplying the number of each type of stone by its average weight gives us the total weight of each type:
- Weight of marvelous stones = 3x × 5kg
- Weight of dangerous stones = 4x × 7kg
The sum of these weights will give us the total weight:
3x × 5kg + 4x × 7kg = 86kg
Solving for x, we get:
15x + 28x = 86
43x = 86
x = 2
Now, to find the number of dangerous stones, we multiply x by 4:
4x = 4 × 2 = 8 dangerous stones.