To determine the possible solutions for the number of minutes Joshua can spend walking and playing basketball, let's consider the given inequalities and possible activity pairs step-by-step. We'll calculate the total calories burned for each pair and verify if it falls within the range of 400 to 600 calories.
The inequalities are:
[tex]\[4w + 5b \geq 400\][/tex]
[tex]\[4w + 5b \leq 600\][/tex]
Activity Pairs:
1. 40 minutes walking, 40 minutes basketball
[tex]\[4(40) + 5(40) = 160 + 200 = 360\][/tex]
This is less than 400, so it does not meet the minimum requirement.
2. 60 minutes walking, 20 minutes basketball
[tex]\[4(60) + 5(20) = 240 + 100 = 340\][/tex]
This is also less than 400, so it does not meet the minimum requirement.
3. 20 minutes walking, 60 minutes basketball
[tex]\[4(20) + 5(60) = 80 + 300 = 380\][/tex]
This is less than 400, so it does not meet the minimum requirement.
4. 50 minutes walking, 50 minutes basketball
[tex]\[4(50) + 5(50) = 200 + 250 = 450\][/tex]
This is within the range of 400 to 600, so it is a valid solution.
5. 60 minutes walking, 80 minutes basketball
[tex]\[4(60) + 5(80) = 240 + 400 = 640\][/tex]
This is more than 600, so it exceeds the maximum limit.
6. 70 minutes walking, 60 minutes basketball
[tex]\[4(70) + 5(60) = 280 + 300 = 580\][/tex]
This is within the range of 400 to 600, so it is a valid solution.
After verifying each activity pair, the possible solutions for the number of minutes Joshua can participate in each activity are:
- 50 minutes walking, 50 minutes basketball
- 70 minutes walking, 60 minutes basketball
