To determine which of the girls is correct, we need to evaluate their equations based on the given scenario.
The given scenario states:
1. One person can plant 4 trees.
2. Five people can together plant 20 trees.
Let [tex]\( x \)[/tex] represent the number of people working, and [tex]\( y \)[/tex] represent the number of trees planted.
Kelly’s equation:
Kelly wrote the equation [tex]\( y = \frac{1}{4} x \)[/tex].
Let's check this for different values of [tex]\( x \)[/tex]:
- For [tex]\( x = 1 \)[/tex] (one person):
[tex]\[
y = \frac{1}{4} \times 1 = \frac{1}{4}
\][/tex]
According to the scenario, one person should plant 4 trees, not [tex]\(\frac{1}{4}\)[/tex] tree. This doesn't match.
- For [tex]\( x = 5 \)[/tex] (five people):
[tex]\[
y = \frac{1}{4} \times 5 = \frac{5}{4} = 1.25
\][/tex]
According to the scenario, five people should plant 20 trees, not 1.25 trees. This doesn't match either.
So, Kelly’s equation is not correct.
Greta’s equation:
Greta wrote the equation [tex]\( y = 4 x \)[/tex].
Let's check this for different values of [tex]\( x \)[/tex]:
- For [tex]\( x = 1 \)[/tex] (one person):
[tex]\[
y = 4 \times 1 = 4
\][/tex]
According to the scenario, one person plants 4 trees, which matches.
- For [tex]\( x = 5 \)[/tex] (five people):
[tex]\[
y = 4 \times 5 = 20
\][/tex]
According to the scenario, five people plant 20 trees, which matches.
So, Greta’s equation is correct.
Conclusion:
The correct options are:
- Greta is correct; [tex]\( 4 = 4 \times 1 \)[/tex] and [tex]\( 20 = 4 \times 5 \)[/tex].
Thus, Greta is correct because her equation [tex]\( y = 4 x \)[/tex] appropriately describes how the number of trees planted ([tex]\( y \)[/tex]) relates to the number of people working ([tex]\( x \)[/tex]).
