## Task 3 - 300613

Lina buys 7 pencils and 8 notebooks and notices that 7 pencils are more expensive than 8 notebooks. Which is more expensive: 10 pencils and 2 notebooks or 11 notebooks and 2 pencils?

Justify your answer!
Answer: 10 pencils and 2 notebooks are more expensive than 11 notebooks and 2 pencils.

Reasoning: If $b$ is the price of a pencil and $h$ is the price of a notebook, then according to Lina's observation, $7 b > 8 h$. (1) From this, it follows that $7 b > 7 h$, (2) thus $b > h$. (3)

From (1) and (3), it follows that $8 b > 9 h$. (4)

If we now increase both $8 b$ and $9 h$ by $2 b + 2 h$, it follows that $10 b + 2 h > 2 b + 11 h$, as stated in the answer.