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Joshua wants to burn at least 400 calories per day, but no more than 600 calories. He does this by walking and playing basketball. Assuming he burns 4 calories per minute walking, [tex]\( w \)[/tex], and 5 calories per minute 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.

- 40 minutes walking, 40 minutes basketball
- 60 minutes walking, 20 minutes basketball
- 20 minutes walking, 60 minutes basketball
- 50 minutes walking, 50 minutes basketball
- 60 minutes walking, 80 minutes basketball
- 70 minutes walking, 60 minutes basketball



Answer :

GinnyAnswer
Let's evaluate each pair of walking and basketball minutes to see which ones meet the criteria of burning between 400 and 600 calories inclusive.

For each pair [tex]\((w, b)\)[/tex]:

1. 40 minutes walking, 40 minutes basketball:
[tex]\[ 4(40) + 5(40) = 160 + 200 = 360 \][/tex]
Joshua burns 360 calories, which is less than 400 calories. This pair does not satisfy the condition.

2. 60 minutes walking, 20 minutes basketball:
[tex]\[ 4(60) + 5(20) = 240 + 100 = 340 \][/tex]
Joshua burns 340 calories, which is less than 400 calories. This pair does not satisfy the condition.

3. 20 minutes walking, 60 minutes basketball:
[tex]\[ 4(20) + 5(60) = 80 + 300 = 380 \][/tex]
Joshua burns 380 calories, which is less than 400 calories. This pair does not satisfy the condition.

4. 50 minutes walking, 50 minutes basketball:
[tex]\[ 4(50) + 5(50) = 200 + 250 = 450 \][/tex]
Joshua burns 450 calories, which is between 400 and 600 calories. This pair satisfies the condition.

5. 60 minutes walking, 80 minutes basketball:
[tex]\[ 4(60) + 5(80) = 240 + 400 = 640 \][/tex]
Joshua burns 640 calories, which is more than 600 calories. This pair does not satisfy the condition.

6. 70 minutes walking, 60 minutes basketball:
[tex]\[ 4(70) + 5(60) = 280 + 300 = 580 \][/tex]
Joshua burns 580 calories, which is between 400 and 600 calories. This pair satisfies the condition.

Therefore, the valid solutions where Joshua can burn between 400 and 600 calories per day are:
- 50 minutes walking and 50 minutes basketball
- 70 minutes walking and 60 minutes basketball

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