Cont.......Find the number of rows and the number of chairs per row. Solve by setting up an equation.Having a lot of trouble with this seemingly easy problem.
Let x be the number of rows. Since The number of chairs per row is two less than twice the number of rows that means that the number of chairs in one row written in equation form would be 2x - 2. so since there are 144 chairs we set up an equation like so: x(2x - 2) = 144; we solve it by first setting it to zero x(2x - 2) = 144 2x^2 - 2x = 144 2x^2 - 2x - 144 = 0 Next we factor the trinomial: 2x^2 - 2x - 144 = 0 2x^2 - 2x - 144 2(x^2 - 2 - 72) 2(x + 8)(x - 9) finally we set what's in parentheses to zero the solve: x + 8 = 0 - 8 -8 x = -8 x - 9 = 0 +9 +9 x = 9 So x is either -8 or 9 however since a negative number cannot be used in a equation -8 can't be an answer to the problem. only 9 (Which is positive) works here. so there are 9 rows of chairs So since earlier we said that x = the number of rows the number of rows is 9. Now to solve for the number of chairs in each row we simply go to where it states 2x - 2 because that expression equals the number of chairs and we substitute 9 for x: 2(9) - 2 18 - 2 16 So there are 16 chairs in each row.
Number of rows is x. Then number of chairs per row is 2x-2 Total number of chairs is 144 and it is a product of two previous numbers. x (2x-2) = 144 2x^2-2x-144=0 x^2 - x - 72 = 0 D=1^2+4*1*72 D=289 (or 17^2) x1 = (1-17)/2 x1 = -8 (negative value is not of interest in this case) x2 = (1+17)/2 x2 = 9 (number of rows) 2x-2 = 2*9-2 = 16 (number of chairs per row) Good luck.
