To determine which girl's equation correctly models the given scenario, we need to examine the relationship between the number of people working and the number of trees planted.
The scenario states:
- One person can plant 4 trees.
- Five people working together can plant 20 trees.
Let's check both equations proposed by Kelly and Greta.
Kelly's Equation:
Kelly proposes [tex]\( y = \frac{1}{4} x \)[/tex]
- By substituting [tex]\( x = 1 \)[/tex] (one person), we get [tex]\( y = \frac{1}{4} \times 1 = \frac{1}{4} \)[/tex]. This means one person plants [tex]\(\frac{1}{4}\)[/tex] of a tree, which is clearly incorrect because one person should plant 4 trees.
- By substituting [tex]\( x = 5 \)[/tex] (five people), we get [tex]\( y = \frac{1}{4} \times 5 = 1.25 \)[/tex]. This means five people plant 1.25 trees, which is also incorrect because five people should plant 20 trees.
Therefore, Kelly's equation does not fit the given scenario.
Greta's Equation:
Greta proposes [tex]\( y = 4 x \)[/tex]
- By substituting [tex]\( x = 1 \)[/tex] (one person), we get [tex]\( y = 4 \times 1 = 4 \)[/tex]. This means one person plants 4 trees, which is correct.
- By substituting [tex]\( x = 5 \)[/tex] (five people), we get [tex]\( y = 4 \times 5 = 20 \)[/tex]. This means five people plant 20 trees, which is correct.
Therefore, Greta's equation correctly models the scenario. Greta is correct; each person plants 4 more trees than the person before them. This also matches the specific result [tex]\(4 = 4 \times 1\)[/tex] and [tex]\(20 = 4 \times 5\)[/tex].
Thus, the correct answer is:
Greta is correct; [tex]$4=4 \times 1$[/tex] and [tex]$20=4 \times 5$[/tex].
