There are only 2 fields on a dartboard with 7 and 9 points. How many times do you need to hit the dart board to score 34 points?

Question

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Answer 1

Let x and y be the number of hits to 7 point field and 9 point field respectively

But x ∈ Z and y ∈ Z, where Z is Integer,

And 7x <= 34  => x ∈ {0,1,2,3,4}

and 9y<=34 => y ∈ {0,1,2,3,4}

but only point (1,3) satisfy the line 7x + 9y such that x and y are integers.

So the solution is 1 --> 7 Points

and 3 --> 9 Points

Therefore total number of times = 1 + 3  = 4

 

 

Answer 2

4 times. On the first shot the score is 7 and the next three shots score 9 each, making 27, 27+7=34.