Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

Rodolfo wants to determine how best to benefit from his weekly workouts. His goal is to burn at least 33003300 calories per week from jogging and playing soccer. He can burn 700700 calories each hour he spends jogging and 600600 calories each hour he spends playing soccer. If Rodolfo's schedule permits him to spend at most 33 hours per week playing soccer and at most 55 total hours per week exercising, which of the following exercise schedules will allow him to meet his weekly goal?\newlineChoose 11 answer:\newline(A) 44 hours playing soccer and 11 hour jogging\newline(B) 11 hour playing soccer and 55 hours jogging\newline(C) 33 hours playing soccer and 22 hours jogging\newline(D) 22 hours playing soccer and 33 hours jogging

Full solution

Q. Rodolfo wants to determine how best to benefit from his weekly workouts. His goal is to burn at least 33003300 calories per week from jogging and playing soccer. He can burn 700700 calories each hour he spends jogging and 600600 calories each hour he spends playing soccer. If Rodolfo's schedule permits him to spend at most 33 hours per week playing soccer and at most 55 total hours per week exercising, which of the following exercise schedules will allow him to meet his weekly goal?\newlineChoose 11 answer:\newline(A) 44 hours playing soccer and 11 hour jogging\newline(B) 11 hour playing soccer and 55 hours jogging\newline(C) 33 hours playing soccer and 22 hours jogging\newline(D) 22 hours playing soccer and 33 hours jogging
  1. Calculate Soccer Calories: Determine the maximum calories Rodolfo can burn from playing soccer.\newlineMaximum hours for soccer = 33 hours\newlineCalories burned per hour playing soccer = 600600 calories\newlineMaximum calories from soccer = Maximum hours for soccer ×\times Calories burned per hour playing soccer\newlineMaximum calories from soccer = 33 hours ×\times 600600 calories/hour\newlineMaximum calories from soccer = 18001800 calories
  2. Calculate Jogging Calories: Determine the maximum calories Rodolfo can burn from jogging.\newlineMaximum hours for jogging = 55 hours - Maximum hours for soccer (since he can exercise for at most 55 hours in total)\newlineMaximum hours for jogging = 55 hours - 33 hours\newlineMaximum hours for jogging = 22 hours\newlineCalories burned per hour jogging = 700700 calories\newlineMaximum calories from jogging = Maximum hours for jogging ×\times Calories burned per hour jogging\newlineMaximum calories from jogging = 22 hours ×\times 700700 calories/hour\newlineMaximum calories from jogging = 5500 calories
  3. Calculate Total Calories: Calculate the total maximum calories Rodolfo can burn with the given constraints.\newlineTotal maximum calories = Maximum calories from soccer + Maximum calories from jogging\newlineTotal maximum calories = 18001800 calories + 14001400 calories\newlineTotal maximum calories = 32003200 calories
  4. Check Goal: Check if the total maximum calories meet Rodolfo's goal.\newlineRodolfo's weekly goal = 33003300 calories\newlineDoes Total maximum calories \geq Rodolfo's weekly goal?\newline32003200 calories \geq 33003300 calories? No.
  5. 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.\newlineLet's evaluate each option:\newline(A) 44 hours playing soccer and 11 hour jogging\newlineCalories burned = (4 hours×600 calories/hour)+(1 hour×700 calories/hour)(4 \text{ hours} \times 600 \text{ calories/hour}) + (1 \text{ hour} \times 700 \text{ calories/hour})\newlineCalories burned = 2400+7002400 + 700\newlineCalories burned = 31003100 calories\newlineDoes this meet the goal? No.\newline(B) 11 hour playing soccer and 55 hours jogging\newlineThis option is not possible because Rodolfo can spend at most 55 total hours per week exercising, and he cannot spend more than 33 hours playing soccer.\newline(C) 33 hours playing soccer and 1100 hours jogging\newlineCalories burned = 1111\newlineCalories burned = 1122\newlineCalories burned = 1133 calories\newlineDoes this meet the goal? No.\newline(D) 1100 hours playing soccer and 33 hours jogging\newlineCalories burned = 1166\newlineCalories burned = 1177\newlineCalories burned = 1188 calories\newlineDoes this meet the goal? Yes.

More problems from Solve proportions: word problems