7.2. There are 30 logs with lengths of 3 and 4 meters, the total length of which is 100 meters. How many cuts can be made to saw the logs into logs of 1 meter length? (Each cut saws exactly one log.)

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# Solution.

First solution. Glue all the logs into one 100-meter log.

To divide it into 100 parts, 99 cuts are needed, 29 of which have already been made.

Second solution. If there were $m$ three-meter logs and $n$ four-meter logs,

then $m+n=30, 3m+4n=100$, from which $m=20, n=10$. Therefore, $20 \cdot 2 + 10 \cdot 3 = 70$ cuts are needed.

Answer. 70.