To solve this question, let's analyze the equations presented by Kelly and Greta, and validate them against the given scenario:
Given information:
- One person was able to plant 4 trees in a given period.
- Five people working together were able to plant 20 trees in the same period.
The equations proposed by Kelly and Greta are:
- Kelly's equation: [tex]\( y = \frac{1}{4}x \)[/tex]
- Greta's equation: [tex]\( y = 4x \)[/tex]
1. Testing Kelly's Equation:
- For 1 person ([tex]\(x = 1\)[/tex]):
[tex]\[
y = \frac{1}{4} \times 1 = \frac{1}{4}
\][/tex]
But the result is 4 trees, not [tex]\(\frac{1}{4}\)[/tex]. Thus, for [tex]\(x = 1\)[/tex], Kelly's equation does not seem to fit.
- For 5 people ([tex]\(x = 5\)[/tex]):
[tex]\[
y = \frac{1}{4} \times 5 = \frac{5}{4}
\][/tex]
And the result should be 20 trees, yet it's not [tex]\(\frac{5}{4}\)[/tex]. Therefore, for [tex]\(x = 5\)[/tex], Kelly's equation also fails to align with the given scenario.
2. Testing Greta's Equation:
- For 1 person ([tex]\(x = 1\)[/tex]):
[tex]\[
y = 4 \times 1 = 4
\][/tex]
This is accurate, as one person plants 4 trees.
- For 5 people ([tex]\(x = 5\)[/tex]):
[tex]\[
y = 4 \times 5 = 20
\][/tex]
This is also correct, as five people plant 20 trees.
Conclusion:
Based on the above calculations:
- Kelly's equation does not fit the given points.
- Greta's equation correctly matches the given points.
Therefore, Greta is correct. She formulated the equation that accurately represents the relationship between the number of people working ([tex]\(x\)[/tex]) and the number of trees planted ([tex]\(y\)[/tex]) in the given scenario. Specifically, her equation is:
[tex]\[
y = 4x
\][/tex]
Hence, Greta's equation shows that each person plants 4 trees, and it accurately reflects the provided data points:
- [tex]\(4 = 4 \times 1\)[/tex] for one person,
- [tex]\(20 = 4 \times 5\)[/tex] for five people.
