Algebra 2 word problem: set up using 3 variables & 3 equations:
"a friend e-mails you the results of a recent high school swim meet. the e-mail states 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 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, second and third?

A) The answer is
x + y + z = 24
3x + 2y + z = 53
x = y + z

x - the number of swimmers in the first place
y - the number of swimmers in the second place
z - the number of swimmers in the third place

1. The e-mail states that 24 individuals placed: x + y + z = 24
2. First place earned 3 points, second place earned 2 points, and third place earned 1 point, earning a combined total of 53 points: 3x + 2y + z = 53
3.  There were as many first-place finishers as second and third-place finishers combined: x = y + z

The system of three equations is:
x + y + z = 24
3x + 2y + z = 53
x = y + z

B) The answer is
12 swimmers in the first place
5 swimmers in the second place
7 swimmers in the third place

(i) x + y + z = 24
(ii) 3x + 2y + z = 53
(iii) x = y + z

Substitute y + z from the third equation into the first one:
(i) x + y + z = 24
(iii) x = y + z

x + x = 24
2x = 24
x = 24 / 2
x = 12


x = y + z
x = 12
y + z = 12
z = 12 - y

3x + 2y + z = 53
3 * 12 + 2y + (12 - y) = 53
36 + 2y + 12 - y = 53
2y - y + 36 + 12 = 53
y + 48 = 53
y = 53 - 48
y = 5

z = 12 - y
z = 12 - 5
z = 7