Answer:
70kg
Step-by-step explanation:
Firstly, because nothing else changed about the treasure chest apart from the amount of treasure when the mass increased, the difference in mass must be the mass of the 1/4 chest of treasure which was added.
712 - 498 = 214kg
Now that we know that 1/4 chest's worth of treasure has a mass of 214kg, we can multiply this by 2 to find the mass of 1/2 a chest of treasure (without the chest):
214 x 2 = 428 kg
We now know that since 1/2 a chest of treasure has a mass of 428kg, the difference between the mass of the chest AND treasure when it is half full must be the mass of the box:
498 (mass of chest and 1/2 chest worth of treasure) - 428 (mass of just 1/2 chest worth of treasure only) = 70kg (mass of chest only)
We can check this by using the other given mass as well. 214 x 3 = 642kg
This means 3/4 of a chest's worth of treasure only, has a mass of 642kg, meaning the extra mass in the 712kg must be the mass of the chest:
712 - 642 = 70kg
The chest has a mass of 70kg.
Hope this helped!
