Madelyn needs to lease out a music studio to record her new album. The studio charges an initial studio-use fee plus an hourly fee for each hour in the studio. The fixed fee to use the studio is $250 and the total cost charged for 5 hours is $500. Write an equation for P, in terms of t, representing the amount of money Madelyn would have to pay to use the studio for t hours.
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Step 1: Identify the given information: - Fixed fee to use the studio: $250 - Total cost for 5 hours: $500 Show more…
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Write a system of equations to determine if and when Gwen will have burned the same number of calories as Tristan and Keith. Then write a system of equations to determine how much each ticket at the fair costs. 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 start 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. 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. 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. 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 and 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. A) Write an equation representing how much Gwen paid. B) Write an equation representing how much Tristan paid. C) Write an equation representing how much Keith paid. 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? Using the Edmentum Graphing tool, graph Gwen's and Keith's equations. Be sure to remove Tristan's equations before adding Keith's equations. Do the two lines intersect? Why or why not? If they intersect, at what point do they intersect? And what does this point mean in terms of the situation? Please draw a graph.
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