Question

An orchard has 651 orange trees. The number of rows exceeds the number of trees per row by 10. How many trees are there in a row

Answer 1

The number of trees in each row is 21.

Explanation:

Let us assume the number of trees in each row = m

So, the number of rows in the orchard = Number of trees in each row + 10

or, total number of trees in each row = (10 +m)

Now, Total number of Trees = Number of Rows x Number of trees in 1 row

⇒ 651 = m (m + 10)

`651 = m^2 + 10m\\\implies  m^2 + 10m - 651 =0\\or,   m^2 + 31m  21m - 651 =0\\or, m(m +31) -21(m+31) =0\\\implies (m +31) (m-21) = 0`

⇒ (m +31) = 0, or (m-21) = 0

⇒ m= -31, or m = 21

Now, as m = The number of trees in each row, so m ≠ -31

So, m = 21

Hence, the number of trees in each row is m = 21.