During a golf match certain number of points are awarded for

During a golf match, certain number of points are awarded for each eagle and a different number for each birdie. No points are awarded for par, and a certain number of points are deducted for each bogey and a different number deducted for each double bogey (or worse). The newspaper report of an important match neglected to mention what these point values were, but did provide the following table of the results: From the information in the table write four equations in terms of four unknowns. Solve the equations for the unknown points awarded for eagles and birdies and points deducted for bogeys and double bogeys.

Solution

This can be Done:

Let Points awarded for Eagles be A
Let Points awarded for Birdies be B
Let Points awarded for Bogeys be C
Let Points awarded for Doubles be D


So, A+2B+C+D = 5--------->Eq(1)
2A+3B+D = 12--------->Eq(2)
A+4B+C = 11--------->Eq(3)
A+3B+2C = 8--------->Eq(4)


Solving (3) and (4) we get [Substract (3) from (4) we get ]

B - C = 3 --------->Eq(5)

Solving (1) and (2) we get [Substract (1) from (2) we get ]

A+B-C = 7 --------->Eq(6)

Solving (5) and (6) we get [Substract (5) from (6) we get ]

A = 4

Put A =4 in Eq(3) we get ,
4B + C = 7--------->Eq(7)

Solving (5) and (7) we get [Add (5) and (7) we get ]

5B = 10 , B = 2

B -C = 3,

So C = -1

A+2B+C+D = 5
=> 4 + 4 -1 + D = 5
=> D = -2



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