SOLUTION: In an office building, a room contains 54 chairs. The number of chairs per row is three less than twice the number of rows. Find the number of rows and the number of chairs per row
Algebra ->
Formulas
-> SOLUTION: In an office building, a room contains 54 chairs. The number of chairs per row is three less than twice the number of rows. Find the number of rows and the number of chairs per row
Log On
Question 167030: In an office building, a room contains 54 chairs. The number of chairs per row is three less than twice the number of rows. Find the number of rows and the number of chairs per row. Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! Let x=number of rows
Let y=number of chairs per row
xy=54----------------------------------eq1
and
y+3=2x---------------------------------eq2
From eq1, we see that y=54/x. Substitute this into eq2:
54/x + 3=2x multiply each term by x
54+3x=2x^2 subtract 2x^2 from each side
-2x^2+3x+54=0 multiply each term by -1
2x^2-3x-54=0---------------------quadratic in standard form and it can be factored
(2x+9)(x-6)=0
x=6--------------------------number of rows
Forget the negative value for x. Rows are positive and besides we can't have fractions of rows
Substitute x=6 into eq1:
6y=54
y=9----------------------------number of chairs per row
CK
The number of chairs per row is three less than twice the number of rows.
9+3=2*6
12=12
also
6*9=54
54=54
