Problem 6.1. The set includes 8 weights: 5 identical round, 2 identical triangular, and one rectangular weight weighing 90 grams.

It is known that 1 round and 1 triangular weight balance 3 round weights. Additionally, 4 round weights and 1 triangular weight balance 1 triangular, 1 round, and 1 rectangular weight.

How much does the triangular weight weigh?
![](https://cdn.mathpix.com/cropped/2024_05_06_8af0c885427e3e323cf9g-12.jpg?height=478&width=420&top_left_y=492&top_left_x=500)
Answer: 60.

Solution. From the first weighing, it follows that 1 triangular weight balances 2 round weights.

From the second weighing, it follows that 3 round weights balance 1 rectangular weight, which weighs 90 grams. Therefore, a round weight weighs $90: 3=30$ grams, and a triangular weight weighs $30 \cdot 2=60$ grams.