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Joshua wants to burn at least 400 calories per day, but no more than 600. He does this by walking and playing basketball. Assuming he burns 4 calories per minute walking, [tex]w[/tex], and 5 calories per minute spent playing basketball, [tex]b[/tex], the situation can be modeled using these inequalities:

[tex]\[
\begin{array}{l}
4w + 5b \geq 400 \\
4w + 5b \leq 600
\end{array}
\][/tex]

Which are possible solutions for the number of minutes Joshua can participate in each activity? Check all that apply.

A. 40 minutes walking, 40 minutes basketball
B. 60 minutes walking, 20 minutes basketball
C. 20 minutes walking, 60 minutes basketball
D. 50 minutes walking, 50 minutes basketball
E. 60 minutes walking, 80 minutes basketball
F. 70 minutes walking, 60 minutes basketball

Sagot :

GinnyAnsweridn
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
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