Question

Cora ran 3 miles last week and will run 7 miles per week from now on. Hana ran 9 miles last week and will run 4 miles per week from now on.

1. Identify what x and y will equal in your equation in the context of the problem.
2. Write a system of equations to describe this scenario.
3. Use Desmos to graph the system of equations you wrote and identify the solution as a coordinate/point. Also identify what the solution means in the context of the problem.

Answer 1

1. In the context of the problem, x will equal the number of weeks and y will equal the total miles run by Cora or Hana in that week.

2. The system of equations for this scenario is:

Cora: y = 7x + 3

Hana: y = 4x + 9.

3. The solution iof the graph of the system of equations will indicate the week when both Cora and Hana will have run the same total distance, and this is given as 2 weeks.

1) Let the number of weeks = x

Let the number of total miles run by Cora or Hana in that week = y

2) The number of miles that Cora ran last week = 3

The number of miles Cora will run per week = 7

The number of miles that Hana ran last week = 9

The number of miles Hana will run per week = 4

Equations:

Cora: y = 7x + 3

Hana: y = 4x + 9

7x + 3 = 4x + 9

3x = 6

x = 2

3) The coordinates of the point of intersection, which represents the number of weeks and the total miles run by both Cora and Hana.

Thus the graph of the system of equations will show two lines intersecting at a point. The solution will be the coordinates of the point of intersection.