SOLUTION: The posted results of a recent high school swim meet state that 24 individuals placed, earning a combined total of 53 points. First place earned 3 points, second place earned 2 poi

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Question 1188041: The posted results of a recent high school swim meet state that 24 individuals placed, earning a combined total of 53 points. First place earned 3 points, second place earned 2 points, and third place earned 1 point. There were as many first-place finishers as second-place and third-place finishers combined.
a. Write a system of three equations that represents how many people finished in each place.
b. How many swimmers finished in first place, in second place, and in third place?
c. Suppose that the athletes scored a combined total of 47 points. Explain why this statement is false and the
solution is unreasonable.
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.


            It is the most stupid instruction to write a system of three equation,
            which can accompany this problem.

            Normally , it is solved using only  ONE  unknown and  ONE  equation. 


Since there were 24 individuals placed, and since  there were as many first-place finishers as second-place and third-place 
finishers combined, it implies that there were 12 first-place finishers and 12 second-place and third-place finishers combined.


Let x be the number of the second-place finishers;  then the number of the third-place finishers is (12-x).


So we have one unknown x and the equation for the total points in the form


    3*12 + 2x + 1*(12-x) = 53.


Simplify and find x


    36 + 2x + 12 - x = 53

         2x      - x = 53 - 36 - 12

              x      = 5.


ANSWER.  There were  12 first-place finishers,  5 second-place finishers and  (12-5) = 7 third-place finishers.

Solved.



Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
x, y, z, how many in first, second, third places


3 points for each of x
2 points for each y
1 point for each z



There were as many first-place finishers as second-place and third-place finishers combined.
.

These two equations

means that and

Here is a system of two equations in two variables.

.
.
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