Aminer descended 1500 feet into a mine. while in the mine, he then rose 1200 feet and then descended 850 feet. what was the miner's net gain or loss in altitude?

Call descending a negative number and rising a positive number.
Then add the numbers.

A miner descended 1500 feet into a mine.
-1500 ft

he then rose 1200 feet
+1200 ft

then descended 850 feet
-850 ft

Now add the three numbers:
-1500 ft + 1200 ft + (- 850 ft) = -1150 ft

Since the sum is a negative number, that means
he had a net loss in altitude of 1150 ft.

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