
(a)
System of three equations representing the number of people finished in each place.
(a)

Answer to Problem 20PPS
System of three equations:
And
And
Explanation of Solution
Given information:
In a high school swim meet,
24 individuals were placed.
Total 53 points were earned.
Such that
1st place earned 3 points
2nd place earned 2 points
3rd place earned 1 point
Let
x people finished 1st
And
y people finished 2nd
And
z people finished 3rd
Now,
The total number of people placed is the sum of number of people placed at each position.
We know that
24 individuals were placed.
Thus,
We also know
Total 53 points were earned.
Since we do not know how many people are there at each position.
Then
Write 3x for 1st place, 2y for 2nd place, z for 3rd place.
Thus,
Also,
According to the statement,
There were as many 1st placed finishers as 2nd and 3rd placed finishers combined.
Thus,
Therefore,
The system of equations we have
And
And
(b)
Swimmers finished in 1st place, in 2nd place, and in 3rd place.
(b)

Answer to Problem 20PPS
12 swimmers finished in 1st place.
5 swimmers finished in 2nd place.
7 swimmers finished in 3rd place.
Explanation of Solution
Given information:
In a high school swim meet,
24 individuals were placed.
Total 53 points were earned.
Such that
1st place earned 3 points
2nd place earned 2 points
3rd place earned 1 point
The original system of equation:
And
And
Substitute Eq. (3) into Eq. (1),
The new equation becomes
Divide both sides by 2:
Now,
Subtract Eq. (1) from Eq. (2), z will be eliminated.
The new equation becomes
Substitute the value of x :
Simplify:
Subtract 24 from both sides:
Now,
Substitute the values of x and y into Eq. (3):
The new equation becomes
Rewrite the equation:
Subtract 5 from both sides:
Therefore,
12 swimmers finished in 1st place, 5 swimmers finished in 2nd place, and 7 swimmers finished in 3rd place.
(c)
Discuss the false e-mailed statement and unreasonable solution.
(c)

Answer to Problem 20PPS
47 points cannot be scored because the number of people at 2nd place cannot be -1.
Explanation of Solution
Given information:
In a high school swim meet,
24 individuals were placed.
According to the e-mailed statement,
Total 47 points were earned instead of 53.
Such that
1st place earned 3 points
2nd place earned 2 points
3rd place earned 1 point
According to the e-mailed statement,
Total 47 points were earned instead of 53.
Then
Eq. (2) becomes Eq. (2’)
Now,
In the system of equations,
Eq. (2) is replaced by Eq. (2’).
Thus,
And
And
Substitute Eq. (3) into Eq. (1),
The new equation becomes
Divide both sides by 2:
Now,
Substitute the value of x in (2’):
Simplify:
Subtract 36 from both sides:
Rewrite the equation:
Substitute Eq. (3):
Substitute the value of x :
Subtract 12 from both sides:
Since the number of people at 2nd place cannot be -1.
Therefore,
It is not possible that 47 points were scored.
Chapter 3 Solutions
Glencoe Algebra 2 Student Edition C2014
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