
a.
To describe: The system of equations in three variables that depicts number of people finished in each place.
a.

Answer to Problem 20PPS
The system of equationsis
Explanation of Solution
Given information:
24 people won a swim meet. They earned a total of 53 points. 3 points were earned by participant who stood first. 2 points were earned by participant who stood second. 1 point was earned by participant who stood third. Total of participants who finished second and third were equal to first place finishers.
Calculation:
It is provided that 24 people won a swim meet. They earned a total of 53 points. 3 points were earned by participant who stood first. 2 points were earned by participant who stood second. 1 point was earned by participant who stood third. Total of participants who finished second and third were equal to first place finishers.
Let number of first place finishers isx , second place finishers be y and third place finishers be z .
It is provided that 24 people won a swim meet., so
They earned a total of 53 points. 3 points were earned by participant who stood first. 2 points were earned by participant who stood second. 1 point was earned by participant who stood third.
So,
Total of participants who finished second and third were equal to first place finishers.
So,
The system of equations obtained is,
b.
To calculate: The number of first, second and third place swimmers.
b.

Answer to Problem 20PPS
The number of first, second and third place swimmers are 12, 5 and 7 respectively.
Explanation of Solution
Given information:
24 people won a swim meet. They earned a total of 53 points. 3 points were earned by participant who stood first. 2 points were earned by participant who stood second. 1 point was earned by participant who stood third. Total of participants who finished second and third were equal to first place finishers.
Calculation:
It is provided that 24 people won a swim meet. They earned a total of 53 points. 3 points were earned by participant who stood first. 2 points were earned by participant who stood second. 1 point was earned by participant who stood third. Total of participants who finished second and third were equal to first place finishers.
Let number of first place finishers isx , second place finishers be y and third place finishers be z .
It is provided that 24 people won a swim meet., so
They earned a total of 53 points. 3 points were earned by participant who stood first. 2 points were earned by participant who stood second. 1 point was earned by participant who stood third.
So,
Total of participants who finished second and third were equal to first place finishers.
So,
The system of equations obtained is,
Take the first and the third equation,
Use the method of elimination to solve the system above.
Subtract both the equations,
Therefore,
Now substitute
Simplify the above system,
Use substitution to solve the above system.
From first equation,
Now substitute
Now, substitute
Therefore, solution is the coordinate pair,
Thus, number of first, second and third place swimmers are 12, 5 and 7 respectively.
c.
To calculate: The number of first, second and third place swimmers if total points scored are 47.
c.

Answer to Problem 20PPS
To compute the problem if total points scored are 47 is not feasible.
Explanation of Solution
Given information:
24 people won a swim meet. They earned a total of 47 points. 3 points were earned by participant who stood first. 2 points were earned by participant who stood second. 1 point was earned by participant who stood third. Total of participants who finished second and third were equal to first place finishers.
Calculation:
It is provided that 24 people won a swim meet. They earned a total of 47 points. 3 points were earned by participant who stood first. 2 points were earned by participant who stood second. 1 point was earned by participant who stood third. Total of participants who finished second and third were equal to first place finishers.
Let number of first place finishers isx , second place finishers be y and third place finishers be z .
It is provided that 24 people won a swim meet., so
They earned a total of 47 points. 3 points were earned by participant who stood first. 2 points were earned by participant who stood second. 1 point was earned by participant who stood third.
So,
Total of participants who finished second and third were equal to first place finishers.
So,
The system of equations obtained is,
Take the first and the third equation,
Use the method of elimination to solve the system above.
Subtract both the equations,
Therefore,
Now substitute
Simplify the above system,
Use substitution to solve the above system.
From first equation,
Now substitute
Now, substitute
Therefore, solution is the coordinate pair,
But number of swimmers cannot be negative.
Thus, to compute the problem if total points scored are 47 is not feasible.
Chapter 3 Solutions
Algebra 2
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