1. A box and 100 identical aluminum balls inside it weigh 510 g. The same box and 100 identical plastic balls inside it weigh 490 g. How much will the box and 20 aluminum balls and 80 plastic balls inside it weigh?
Solution. Method 1. Let's take 4 boxes with plastic balls and one with aluminum ones. Their total weight is 4*490+510=2970 (g). Redistribute the balls so that each box contains 20 aluminum and 80 plastic balls. Then the weight of all boxes is the same, and the weight of one box with balls is $2970: 5=494(g)$.

Method 2. (For those familiar with decimal fractions) By dividing the weight of each box with balls by 100, we get the weight of one ball plus $1 / 100$ of the weight of the box: 5.1 g and 4.9 g. Adding the weight of 20 aluminum balls ($20 \times 5.1$) and 80 plastic balls ($80 \times 4.9$), we get their total weight together with the box, since there are 100 balls in total: 102 + $392=494(g)$.

Criteria. Any correct solution: 7 points.

If Method 2 is provided, where it is assumed by default that the box is weightless (a special case), and the correct answer is obtained. There is no justification that all cases where the box has weight reduce to this special case: 2 points. (If there is justification - this is a correct solution)

Only the correct answer is provided: 1 point.