Solving Systems of Equations Graphically Gwen, Tristan, and Keith like to work out at the gym. They each have an app on their phone that estimates the calories they burn. By the time Tristan and Keith started exercising, Gwen had already burned 100 calories. Gwen burns 10 calories every minute, Tristan burns 125 every 10 minutes, and Keith burns 300 calories every 30 minutes. Let x represent the number of minutes since Tristan and Keith started exercising and y represent the number of app-estimated calories burned.
Part A
Write an equation representing Gwen’s calories burned with respect to the number of minutes since Tristan and Keith started exercising.
Part B
Write an equation representing the number of calories Tristan has burned with respect to the number of minutes since he and Keith started exercising.
Part C
Write an equation representing the number of calories Keith has burned with respect to the number of minutes since he and Tristan started exercising.
Part D
Using the Edmentum Graphing Tool, graph Gwen’s and Tristan’s equations. Hint: To create the graph, select the correct relationship and then enter the values for the variables. You will need to change the scales for the x- and y-axes. When deciding the scale, ask yourself what x and y stand for, and what would be reasonable amounts for their minimum and maximums. Do the two lines intersect? Why or why not? What does this mean in terms of the situation? If the lines intersect, at what point do they intersect and what does this point mean in terms of the situation? Paste a screenshot of your graph in the space provided.
Part E
Using the Edmentum Graphing Tool, graph Gwen’s and Keith’s equations. Be sure to remove Tristan’s equation before adding Keith’s equation. Do the two lines intersect? Why or why not? What does this mean in terms of the situation? If they intersect, at what point do they intersect and what does this point mean in terms of the situation? Paste a screenshot of your graph in the space provided.