8.2. The magpie-crow was cooking porridge and feeding her chicks. The third chick received as much porridge as the first two combined. The fourth one received as much as the second and third. The fifth one received as much as the third and fourth. The sixth one received as much as the fourth and fifth. And the seventh one got nothing - the porridge ran out! It is known that the fifth chick received 10 grams of porridge. How much porridge did the magpie-crow cook?
Answer: 40 g.

Solution. Let the first chick receive $m$ g of porridge, and the second chick $-n$ g. Then the third chick received $m+n$ (g), the fourth chick $-m+2n$ (g), the fifth chick $-2m+3n$ (g), and the sixth chick $-3m+5n$ (g). Therefore, the total amount of porridge was: $m+n+(m+n)+(m+2n)+(2m+3n)+(3m+5n)=8m+12n=4(2m+3n)$ (g). This is four times the amount that the fifth chick received, so the magpie cooked $10 \cdot 4=40$ (g) of porridge.

## Grading Criteria:

+ a complete and justified solution is provided

✓ the correct answer is obtained by considering specific examples

✓ two variables are reasonably introduced and expressions for the amount of porridge received by each chick are written (possibly with an error), but the solution is not completed to the correct answer

- only the answer is provided
- the problem is not solved or is solved incorrectly