Investigation 16543

There were 16 more forwards than defensemen on the hockey team. As part of the investigation, the coach was tasked with dismissing a quarter of the attackers and four defenders from the team. After the release, 22 forwards and defensemen remained on the team. How many hockey players were originally on the team?

Correct answer:

n =  32

Step-by-step explanation:

n = u+o
u = 16+o
22 = u+o -u/4-4

n-o-u = 0
o-u = -16
4o+3u = 104

Pivot: Row 2 ↔ Row 3
n-o-u = 0
4o+3u = 104
o-u = -16

Row 3 - 1/4 · Row 2 → Row 3
n-o-u = 0
4o+3u = 104
-1.75u = -42


u = -42/-1.75 = 24
o = 104-3u/4 = 104-3 · 24/4 = 8
n = 0+o+u = 0+8+24 = 32

n = 32
o = 8
u = 24

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