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There are 600 students. Every chair is filled. Each row contains the same number of chairs. If you add five more chairs to each row there would be four fewer rows. How many chairs are in each row?
Wiki User
∙ 12y ago
to begin with there are 24 rows and 25 chairs in a row
r = number of rows
c = number of chairs in a row
600 chairs total: RC = 600
Adding 5 more chairs allows you to remove 4 rows: (c + 5) (r - 4) = 600
(c + 5) (r - 4) = RC
RC + 5r - 4c - 20 = RC
5r - 4c - 20 = 0
5r - 4(600/r) - 20 = 0
5r^2 - 2400 - 20r = 0
5r^2 - 20r - 2400 = 0
r^2 - 5r - 480 = 0
(r-24) (r+20) = 0
r = 24 or r = -20
If r = 24, then c = 600/24 = 25
24 rows of 25 chairs each to begin with
Check your work: 24-4 = 20, 25+5 = 30, 30*20 = 600 Check.
Wiki User
∙ 12y ago
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