Some students planted $100$ trees. Out of the $100$ trees planted, the number of non-fruit-bearing trees was one more than twice the number of fruit-bearing trees. How many fruit-bearing and non-fruit-bearing trees did they plant?

33 and 67

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34 and 66

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35 and 65

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32 and 68

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Solution

The correct option is A $33 and 67$
Let $x$ be the number of fruit-bearing trees.

According to the question, the number of non-fruit-bearing trees should be $1 + 2 x .$
Total number of trees $= 100$
$\Rightarrow$ Number of fruit-bearing trees $+$ number of non-fruit-bearing trees $= 100$
$\Rightarrow$ $x + (1 + 2 x) = 100$
The above algebraic equation represents the scenario given in the question.

Solving this equation to find the value of $x$ ,
$x + (1 + 2 x) = 100$
$\Rightarrow 3 x + 1 = 100$

Subtracting $1$ from both sides of the equation, we get
$\Rightarrow 3 x + 1 - 1 = 100 - 1$
$\Rightarrow 3 x = 99$

Dividing both sides of the equation by $3$ , we get
$\Rightarrow \frac{3 x}{3} = \frac{99}{3}$
$\Rightarrow x = 33$

The number of fruit-bearing trees planted is $33.$

Number of non-fruit-bearing trees planted $= 1 + 2 x$
$= 1 + 2 \times 33 = 1 + 66$
$= 67$

The number of non-fruit-bearing trees planted is $67.$

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Some students planted 100 trees. Out of the 100 trees planted, the number of non-fruit-bearing trees was one more than twice the number of fruit-bearing trees. How many fruit-bearing and non-fruit-bearing trees did they plant?

Some students planted $100$ trees. Out of the $100$ trees planted, the number of non-fruit-bearing trees was one more than twice the number of fruit-bearing trees. How many fruit-bearing and non-fruit-bearing trees did they plant?