The girls agree that x represents the number of people working and y represents the number of trees planted. Kelly wrote the equation y = one-fourth x, and Greta wrote the equation y = 4 x. Which person is correct, and why?

Complete question :

Kelly and Greta are asked to write an equation for the scenario below. “One person was able to plant 4 trees in the same amount of time that 5 people working together were able to plant 20 trees.” The girls agree that x represents the number of people working and y represents the number of trees planted. Kelly wrote the equation y = one-fourth x, and Greta wrote the equation y = 4 x . Which person is correct, and why? Kelly is correct; each person plants more trees than the person before them. Kelly is correct; and . Greta is correct; each person plants 4 more trees than the person before them. Greta is correct; and

Greta is correct

Step-by-step explanation:

Given the scenario :

One person was able to plant 4 trees in the same amount of time that 5 people working together were able to plant 20 trees.

Time taken by one person to plant 4 trees = time taken by 5 people to plant 20 trees

This means that, the people (tree planters) are working at the same rate and hence , 1 person can plant 4 trees :

That is ; number of trees plants equals 4 times the number of people

x = number of people working

y = number of trees planted

y = 4x

Kelly's equation :

y = 1/4 x

Greta's equation:

y = 4x

Hence, Greta is correct

We can use Greta's equation to verify the statement above;

Number of trees planted = 20

Number of people = 5

Using : y = 4x ; y = 4(5) ; y = 20

Also, number of people = 1

Trees planted = 4

y = 4x ; y = 4(1) ; y = 4

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