Rodolfo wants to determine how best to benefit from his weekly workouts. His goal is to burn at least 3300 calories per week from jogging and playing soccer. He can burn 700 calories each hour he spends jogging and 600 calories each hour he spends playing soccer. If Rodolfo's schedule permits him to spend at most 3 hours per week playing soccer and at most 5 total hours per week exercising, which of the following exercise schedules will allow him to meet his weekly goal?Choose 1 answer:(A) 4 hours playing soccer and 1 hour jogging(B) 1 hour playing soccer and 5 hours jogging(C) 3 hours playing soccer and 2 hours jogging(D) 2 hours playing soccer and 3 hours jogging
Q. Rodolfo wants to determine how best to benefit from his weekly workouts. His goal is to burn at least 3300 calories per week from jogging and playing soccer. He can burn 700 calories each hour he spends jogging and 600 calories each hour he spends playing soccer. If Rodolfo's schedule permits him to spend at most 3 hours per week playing soccer and at most 5 total hours per week exercising, which of the following exercise schedules will allow him to meet his weekly goal?Choose 1 answer:(A) 4 hours playing soccer and 1 hour jogging(B) 1 hour playing soccer and 5 hours jogging(C) 3 hours playing soccer and 2 hours jogging(D) 2 hours playing soccer and 3 hours jogging
Calculate Soccer Calories: Determine the maximum calories Rodolfo can burn from playing soccer.Maximum hours for soccer = 3 hoursCalories burned per hour playing soccer = 600 caloriesMaximum calories from soccer = Maximum hours for soccer × Calories burned per hour playing soccerMaximum calories from soccer = 3 hours ×600 calories/hourMaximum calories from soccer = 1800 calories
Calculate Jogging Calories: Determine the maximum calories Rodolfo can burn from jogging.Maximum hours for jogging = 5 hours - Maximum hours for soccer (since he can exercise for at most 5 hours in total)Maximum hours for jogging = 5 hours - 3 hoursMaximum hours for jogging = 2 hoursCalories burned per hour jogging = 700 caloriesMaximum calories from jogging = Maximum hours for jogging × Calories burned per hour joggingMaximum calories from jogging = 2 hours ×700 calories/hourMaximum calories from jogging = 50 calories
Calculate Total Calories: Calculate the total maximum calories Rodolfo can burn with the given constraints.Total maximum calories = Maximum calories from soccer + Maximum calories from joggingTotal maximum calories = 1800 calories + 1400 caloriesTotal maximum calories = 3200 calories
Check Goal: Check if the total maximum calories meet Rodolfo's goal.Rodolfo's weekly goal = 3300 caloriesDoes Total maximum calories ≥ Rodolfo's weekly goal?3200 calories ≥3300 calories? No.
Evaluate Options: Since the total maximum calories do not meet Rodolfo's goal, we need to adjust the hours spent on each activity to see if any of the given options (A, B, C, D) allow him to meet or exceed the goal.Let's evaluate each option:(A) 4 hours playing soccer and 1 hour joggingCalories burned = (4 hours×600 calories/hour)+(1 hour×700 calories/hour)Calories burned = 2400+700Calories burned = 3100 caloriesDoes this meet the goal? No.(B) 1 hour playing soccer and 5 hours joggingThis option is not possible because Rodolfo can spend at most 5 total hours per week exercising, and he cannot spend more than 3 hours playing soccer.(C) 3 hours playing soccer and 10 hours joggingCalories burned = 11Calories burned = 12Calories burned = 13 caloriesDoes this meet the goal? No.(D) 10 hours playing soccer and 3 hours joggingCalories burned = 16Calories burned = 17Calories burned = 18 caloriesDoes this meet the goal? Yes.
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