To analyze the scenario carefully:
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The scenario states that "one person was able to plant 4 trees." This means that if 1 person works, they plant 4 trees.
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The scenario also states that "5 people working together were able to plant 20 trees." This implies that when you have 5 people, they collectively plant 20 trees.
Now, let’s break down the equations suggested by Kelly and Greta:
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Kelly's equation: \( y = \frac{1}{4}x \) suggests that each person plants one-fourth of the number of trees represented by \( x \). This interpretation does not accurately reflect the situation, since we know from the scenario that 1 person plants 4 trees and not one-fourth of the trees.
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Greta's equation: \( y = 4x \) suggests that for each person \( x \), they plant 4 trees. This matches the provided information: if 1 person plants 4 trees (when \( x = 1 \), \( y = 4 \)) and if there are 5 people, that would be \( y = 4(5) = 20 \), which aligns with the scenario given that 5 people plant 20 trees.
Given the analysis, Greta is correct because her equation accurately represents how many trees are planted based on the number of people working. The correct reasoning is represented through the understanding that each person contributes to planting 4 more trees, resulting in her equation \( y = 4x \).
Therefore, the correct option is Greta is correct; \( 4 = 4 \) times \( 1 \) and \( 20 = 4 \) times \( 5 \).
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