A certain number of trees are planted in rows and columns. If 3 trees are planted
more in each row then number of columns will decrease by 2. If 5 trees are planted
less in each row then number of columns will increase by 6. Find the number of
trees planted in each row and number of columns.[linear equation in 2 variables}
Answers
Given :- A certain number of trees are planted in rows and columns. If 3 trees are planted more in each row then number of columns will decrease by 2. If 5 trees are planted less in each row then number of columns will increase by 6.
Solution :-
Let number of trees planted in rows are x and in column are y .
so,
→ Total trees = x * y = xy .
A/q,
→ (x + 3) * (y - 3) = xy
→ xy - 3x + 3y - 9 = xy
→ 3y - 3x = 9 -------- Eqn.(1)
and,
→ (x - 5) * (y + 6) = xy
→ xy + 6x - 5y - 30 = xy
→ 6x - 5y = 30 ------ Eqn.(2)
multiply Eqn.(1) by 2 and adding both,
→ (6x - 5y) + 2(3y - 3x) = 30 + 2*9
→ 6x - 6x - 5y + 6y = 30 + 18
→ y = 48
putting value of y in Eqn.(1),
→ 3*48 - 3x = 9
→ 3x = 144 - 9
→ 3x = 135
→ x = 45 .
therefore, number of trees in each row are 45 and number of trees in each column are 48 .
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