IF YOU ANSWER MORE THEM ONE ILL GIVE BRAINLIEST AND LOTS OF POINTS PLEASE DONT ANSWER IF YOUR NOT GOING TO BE HELPFUL THANKS Introduction Gwen is exercising at the gym. After a while, Tristan and Keith arrive to exercise with her. After they finish exercising, they are going to go to the fair.
In this activity, you will write a system of equations to determine if and when Gwen will have burned the same number of calories as Tristan and Keith. Then, you will write a system of equations to determine how much each ticket at the fair costs.


Directions and Analysis Task 1: 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.

a. Write an equation representing Gwen’s calories burned with respect to the number of minutes since Tristan and Keith started exercising.

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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.

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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.

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d. Using the Edmentum Graphing Tool, graph Gwen’s and Tristan’s equations. Hint: 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.

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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.

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Task 2: Solving Systems of Equations Algebraically
After Gwen, Tristan, and Keith finish exercising, they go to the fair. At the fair, they each pay the entry fee and also buy tickets they can use for food or rides. Gwen pays the entry fee and buys 10 tickets. It costs her a total of $30. Tristan pays the entry fee and buys 15 tickets. It costs him a total of $40. Keith pays the entry fee and buys 10 tickets. It costs him a total of $30. In this task, you will create a system of equations and find the cost of each ticket. Let x represent the entry fee and y represent the cost of each ticket in dollars.

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a. Write an equation representing how much Gwen paid.

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b. Write an equation representing how much Tristan paid.

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c. Write an equation representing how much Keith paid.

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d. Which two equations could you use as a system to find the cost of the entry fee and the cost of each ticket? Why?

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e. Solve the system you found in part d. Did you use elimination or substitution? What was the entry fee, and how much did each ticket cost?

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f. What do you need to do to the equations so you can put them into the Edmentum Graphing Tool? Put the equations into the Edmentum Graphing Tool. Paste a screenshot of your graph in the space provided. Do you get the same solution as when you solved it algebraically?

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