SOLUTION: A man is setting out 180 plants in rows, each row having the same number of plants in it. If there were 40 more plants in each row, the man would need 6 fewer rows. How many rows a

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Question 184159: A man is setting out 180 plants in rows, each row having the same number of plants in it. If there were 40 more plants in each row, the man would need 6 fewer rows. How many rows are there?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=number of rows to start with
x-6=new number of rows after the plants are redistributed
Then 180/x=number of plants per row
Add 40 more plants to each row and we have
(180/x)+40=(180+40x)/x---- new number of plants per row
(new # plants/row)(new # rows)=180
(180+40x)/x * (x-6)=180 or
(x-6)(180+40x)=180x expand left side using FOIL
180x+40x^2-1080-240x=180x subtract 180x from each side
40x^2-240x-1080=0 divide each term by 40
x^2-6x-27=0----quadratic in standard form and it can be factored
(x-9)(x+3)=0
Disregard negative value for x; rows are positive
x=9---------------number of rows to start with
CK
180/9=20 plants/row
20+40=60 plants/row
60*(9-6)=180
180=180
Hope this helps---ptaylor