Students in grade 7 plant 100 trees in the school garden. The trees planted can be classified as fruit and non-fruit trees. If the number of non-fruit trees planted is one more than twice the number of fruit trees, then how many fruit trees and non-fruit trees did they plant?

67, 33

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66, 34

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33, 67

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50, 50

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Solution

The correct option is C $33, 67$
Let $x$ be the number of fruit trees.
Number of non-fruit trees = $1 + 2 x$
Total number of trees = number of fruit trees + number of non-fruit trees
$\Rightarrow 100 = x + (1 + 2 x)$
$\Rightarrow 100 = x + 2 x + 1$ [Using commutative property]
$\Rightarrow 100 = 3 x + 1$
$\Rightarrow 100 - 1 = 3 x + 1 - 1$ [Subtracting both sides by 1]
$\Rightarrow 99 = 3 x$
$\Rightarrow \frac{99}{3} = \frac{3 x}{3}$ [Dividing both sides by 3]
$\Rightarrow x = 33$
Number of fruit trees = 33
Number of non-fruit trees $= 1 + 2 x$
$= 1 + 2 \times 33$
$= 1 + 66$
$= 67$

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