Cynthia has an exercise regimen at the local gym that includes using a treadmill, stair machine, and cycle. According to an exercise website, a 130-lbd person like Cynthia will burn, on average, about 600 calories per hour running on a treadmill, about 500 calories per hour on the stair machine, and about 300 calories per hour on the sycle. Cynthia wants to spend 7 hours a week in the gym, and would like to spend twice as much time on the stair machine as the cycle. She wants to burn 3300 calories a week at the gym. Is this possible? (a) Write the system of equations that describe the problem. Let t be the number of hours she spends on the treadmill, s be the number of hours she spends on the stair machine, and c be the number of hours she spends on the cycle. Make sure to use the variables from the drop down menu. Calories equation: Time equation: Machines equation: (b) Use an online calculator to solve the system of equations. Put your answer into context by entering the values in the sentence below. Make sure to enter your answers as decimals, not fractions. Cynthia needs to spend hours per week on the treadmill, hours per week on the stair machine, and hours per week on the cycle to reach her goal of burning 3300 calories a week. (c) Cynthia has several exams and due dates in the coming week and can only spend 4.5 hours at the gym. Modify the equations as needed and solve the new system of equations. Write down the solution from the online calculator as a sentence (like in part b) in the window below and state whether or not Cynthia will be able to reach the goal of burning 3300 calories in that week. Give a reason for your answer.