in an Orchard the number of tree in each column is 5 more than that in each row find a number of tree in each column if the total number of tree is 1400
Answers
Given : in an orchard the number of trees in each column is 5 more than that in each row .
Total number of trees is 1400
To Find : the number of trees in each column,
Solution:
number of trees in each column = x
number of trees in each column is 10 more than that in each row .
number trees in each row = x - 5
Total number of trees = x(x -5)
= x² - 5x
x² - 5x = 1400
=> x² - 5x - 1400 =
=> x² - 40x + 35x - 1400 = 0
=> (x - 40)(x + 35) = 0
=> x = 40
number of trees in each column = 40
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Answer:
The number of trees in a column is 40.
Step-by-step explanation:
Let the number of trees in a row be x.
The number of trees in a column =(x+5−−−−−)
Total number of trees =x(x+5)−−−−−−−
Total number of trees =1400−−−− ….(Given )
∴x(x+5)=1400−−−−−−−−−−−−−
∴x2+5x−1400=0
∴x2+40x−35x−1400=0
∴x(x+40)−35(x+40)=0
∴(x+40)(x−35)=0
∴x+400 or x−35=0
∴x=−40 or x=35
But the number of trees cannot be negative.
∴x−40 is unacceptable
∴x=35 ∴x+5=35+5=40