Question & Answer
QUESTION

People of Sundargram planted a total of 102 trees in the village garden. Some of the trees were fruit trees. The number of non-fruit trees were two more than three times the number of fruit trees. What was the number of fruit trees planted?

ANSWER Verified Verified
Hint: First of all, consider the number of trees as a variable. Then find the number of non-fruit trees in terms of fruit trees by the given conditions. Equate the sum of fruit trees and non-fruit trees to the total number of trees.

Complete step-by-step answer:
Let the number of fruit trees is \[t\].
Given the number of non-fruit trees were two more than three times the number of fruit trees
So, number of non-fruit trees \[ = 3t + 2\]
Since the total number of trees is 102, we have
\[
   \Rightarrow t + 3t + 2 = 102 \\
   \Rightarrow 4t + 2 = 102 \\
   \Rightarrow 4t = 102 - 2 \\
   \Rightarrow 4t = 100 \\
   \Rightarrow t = \dfrac{{100}}{4} \\
  \therefore t = 25 \\
\]
Thus, the number of fruit trees is 25.

Note: According to the given conditions the number of non-fruit trees is more than fruit trees. The value of \[t\] cannot be negative. The total number of non-fruit trees and fruit trees should be equal to the total number of trees.