# Task 7.2

There are 30 logs, the lengths of which are 3 or 4 meters, and their total length is one hundred meters. How many cuts are needed to saw all these logs into pieces 1 meter long? (Each cut saws exactly one log).

Points 7

#
# Answer:

70

## Solution

## First Method

The total length of the logs is 100 meters. If it were a single log, 99 cuts would be needed. Since there are 30 logs, 29 cuts have already been made. Therefore, another $99-29=70$ cuts are needed.

## Second Method

Let's find the number of logs of each type. If all the logs were 3 meters long, their total length would be 90 meters. Since the total length is 100 meters, there are 10 logs that are 4 meters long and 20 logs that are 3 meters long. For each 4-meter log, three cuts are needed, and for each 3-meter log, two cuts are needed. In total: $10 \times 3 + 20 \times 2 = 70$ cuts.

Additional criteria for evaluation.

"4 or 5 points" A generally correct reasoning is provided, but a computational error is made.

"2 or 3 points" Only the correct answer is provided or the correct answer is obtained from a specific example.