Puzzle 99 - Solution

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 This was the question.

 Two friends were playing a ring toss game where you throw 10 rings over the tops of cylinders 15 feet away. For each ring that goes over a cylinder, you receive 5 points. For each ring that misses, you lose 3 points. One of the friends scored 26 and the other scored 18. How many rings did each have that were successful tosses?

Solution:

Let us say first friend had x successful ring tosses and y failed ones.

5x - 3y = 26 -----(i)
  x+y = 10 --------(ii) ( because each person can throw only 10 tosses. )

Multiplying the equation (ii) by 3, we get

3x+3y = 30 ----(iii)

Adding (i) and  (iii) we get

8x = 56, x =56/8 = 7
y = 10-x = 10-7 =3

First person threw 7 rings over the cylinder and 3 rings which missed the cylinder. 


For the second person, the equations are

 5x-3y=18 ----(i)
  x+y=10   -----(ii)

Multiplying (ii) by 3 and adding (i) and (ii) we get, 

5x-3y=18
3x+3y=30
8x=48
x=48/8 = 6
y=10-x=10-6=4

Second person threw 6 rings over the cylinder and 4 rings which missed the cylinder.


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