
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
Additional Math Textbook Solutions
Elementary Statistics: Picturing the World (7th Edition)
Elementary Statistics (13th Edition)
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Algebra and Trigonometry (6th Edition)
University Calculus: Early Transcendentals (4th Edition)
- Safari File Edit View History Bookmarks Window Help Ο Ω OV O mA 0 mW ర Fri Apr 4 1 222 tv A F9 F10 DII 4 F6 F7 F8 7 29 8 00 W E R T Y U S D பட 9 O G H J K E F11 + 11 F12 O P } [arrow_forwardSo confused. Step by step instructions pleasearrow_forwardIn simplest terms, Sketch the graph of the parabola. Then, determine its equation. opens downward, vertex is (- 4, 7), passes through point (0, - 39)arrow_forward
- In simplest way, For each quadratic relation, find the zeros and the maximum or minimum. a) y = x 2 + 16 x + 39 b) y = 5 x2 - 50 x - 120arrow_forwardIn simplest terms and step by step Write each quadratic relation in standard form, then fi nd the zeros. y = - 4( x + 6)2 + 36arrow_forwardIn simplest terms and step by step For each quadratic relation, find the zeros and the maximum or minimum. 1) y = - 2 x2 - 28 x + 64 2) y = 6 x2 + 36 x - 42arrow_forward
- Write each relation in standard form a)y = 5(x + 10)2 + 7 b)y = 9(x - 8)2 - 4arrow_forwardIn simplest form and step by step Write the quadratic relation in standard form, then fi nd the zeros. y = 3(x - 1)2 - 147arrow_forwardStep by step instructions The path of a soccer ball can be modelled by the relation h = - 0.1 d 2 + 0.5 d + 0.6, where h is the ball’s height and d is the horizontal distance from the kicker. a) Find the zeros of the relation.arrow_forward
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education





