SOLUTION: In an office building, a room contains 48 chairs. The number of chairs per row is 10 less than twice the number of rows. find the number of rows. Thanks!

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Question 378932: In an office building, a room contains 48 chairs. The number of chairs per row is 10 less than twice the number of rows. find the number of rows.
Thanks!
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the number of chairs/row and r be the number of rows.
You are told
x%2Ar+=+48
and
x+=+2r+-+10
So
x%2Ar+=+48
%282r+-+10%29+%2A+r+=+48
2r%5E2+-+10r+=+48
2r%5E2+-10r+-+48+=+0
r%5E2+-+5r+-+24+=+0
%28r+-+8%29%28r+%2B+3%29+=+0
So r can be either 8 or -3. Since the number of rows can't be negative,
there must be 8 rows.
If there are 8 rows, then x%2A8+=+48
thus x+=+6
8 rows of 6 chairs each