How Many Hits Out of 100 Shots? — Can you solve it?

84. How Many Hits Out of 100 Shots?

In a shooting game the player receives +1 point for every hit and –1 point for every miss. A marksman takes exactly 100 shots and finishes the game with a total of 30 points.

How many of his shots hit the target?

Added 1 October 2009

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Hint:

Let h be the number of hits and m the number of misses. You know both h + m and h − m.

Solution:

Let h = number of hits and m = number of misses.

1. Total shots: h + m = 100
2. Total score: (+1)×h + (–1)×m = 30, so h − m = 30

Add the two equations: (h + m) + (h − m) = 100 + 30 → 2h = 130 → h = 65.

Therefore the marksman hit the target 65 times (and missed 35 times).

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