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Question 999185: please help me I never took this until now and is like I am learning a foreign language. Please help me and show or explain all steps.
On an 18-hole golf course there are par-3holes, par 4 hole par-5 holes. A golfer who shoos par on every hole has a score of 72. How many of each type of hoe are there on the golf course. I said 6
A.) Is there enough information to answer this question? Why or Why not?
B) What if we also know that the sum of the number of par-3 holes and par-5 holes is 8? Is this enough information?yes What system of equation? parabola
C) Write the augmented matrix for this system and solve it using the Gaussian Elimination Method. Show all steps! Don't forget to answer the original question.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! let x be number of par3's, y be number of par4's, z = number of par5's, then
3x + 4y + 5z = 72
x + y + z = 18
A) not enough info to answer question since we have two equations in three unknowns - we need three equations in three unknowns.
B) x + z = 8, now we have enough information
note that these are linear equations (exponents are 1)
C) augmented matrix is
3 4 5 72
1 1 1 18
1 0 1 8
Gaussian elimination method
subtract row 3 from row 2
3 4 5 72
0 1 0 10
1 0 1 8
multiply row 3 by 3 and subtract from row 1
0 4 2 48
0 1 0 10
1 0 1 8
multiply row 2 by 4 and subtract from row 1
0 0 2 8
0 1 0 10
1 0 1 8
divide row 1 by 2
0 0 1 4
0 1 0 10
1 0 1 8
subtract row 1 from row 3
0 0 1 4
0 1 0 10
1 0 0 4
***********************************************************
x = 4, y = 10, z = 4
***********************************************************
note that
x + z = 8
3*4 + 4*10 + 5*4 = 72
12 + 40 + 20 = 72
72 = 72
our answers check
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