Linear equations

Algebra Level 2

In a shooting competition a marksman receives 50 paise if he hits the mark and pays 20 paise if he misses. He tried 60 shots and was paid 130 paise .How many times did he hit the mark?


The answer is 19.

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

let the number of times he hits the mark be x

therefore, number of times he misses =(60-x)

amount he gets for hitting = 50

amount he pays for missing = 20

as per question

50(x) - 20(60-x) = 130

Or, 50x - 1200 +20x = 130

Or,70x = 130 + 1200

Or,70x = 1330

Or,x = 1330\70

Or,x=19

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Using two variables was pretty easy though. Also nice solution.

Saraswat Bhattacharya - 4 years, 1 month ago

Let h h be the number of times he hits the mark and m m be the number of times he misses the mark. Then

h + m = 60 h+m=60 or m = 60 − h m=60-h ( 1 ) \color{#D61F06}(1)

50 h − 20 m = 130 50h-20m=130 ( 2 ) \color{#D61F06}(2)

Substitute ( 1 ) \color{#D61F06}(1) in ( 2 ) \color{#D61F06}(2) . We have

50 h − 20 ( 60 − h ) = 130 50h-20(60-h)=130

50 h − 1200 + 20 h = 130 50h-1200+20h=130

70 h = 130 + 1200 70h=130+1200

70 h = 1330 70h=1330

h = 19 h=19

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