Question

In a mango groove, the trees are planted in horizontal and vertical rows. There are 8 more trees in each horizontal row than in the vertical row. Altogether there are 1280 trees. Find the number of trees in each horizontal row.

Answer 1

Hint: We can make an equation using a variable and proceed according to the question. As both the quantities are dependent (one 8 more than the other), the equation will be in one variable.

Complete step-by-step answer:
Let the number of trees in each vertical row be x
It is given that each horizontal row has 8 more trees than each vertical row, thus
Number of trees in each horizontal row is x + 8
Now, the total number of trees = 1280
Number of trees in each horizontal row + Number of trees in each vertical row = 1280
$\Rightarrow$ x + x + 8 = 1280
$\Rightarrow$ 2x + 8 = 1280
$\Rightarrow$ 2x = 1280 – 8
$\Rightarrow$ 2x = 1272
$\Rightarrow$ x = 636
Vertical rows x = 636
Horizontal rows x +8 = 636 + 8
 = 644
Therefore, the number of trees in each vertical row is 636 and in each horizontal row is 644.

Note: The equation formed here is a linear equation in one variable, linear because the maximum power of x is 1 and the value of x obtained is one.
When the linear equation is in two variables, there will be two values of x.
Points to be kept in mind while solving linear equations:
Simplify equations considering both right hand side (RHS) and left hand side (LHS).
The variable is isolated, fractions are reduced if any and its value is calculated.