Question

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, w, and 5 calories per minute spent playing basketball, b, the situation can be modeled using these inequalities: 4w + 5b ≥ 400 4w + 5b ≤ 600 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 1

D & F

Explanation:

Answer 2

The possible solutions are:

50 minutes walking, 50 minutes basketball

70 minutes walking, 60 minutes basketball

Explanation:

These following inequalities need to be respected:

4w + 5b ≥ 400

4w + 5b ≤ 600

40 minutes walking, 40 minutes basketball

This means that w = 40, b = 40. So

4w + 5b = 4*40 + 5*40 = 360

This is lower than 400, so it is not a possible solution.

60 minutes walking, 20 minutes basketball

This means that w = 60, b = 20. So

4w + 5b = 4*60 + 5*20 = 340

This is lower than 400, so it is not a possible solution.

20 minutes walking, 60 minutes basketball

This means that w = 20, b = 60. So

4w + 5b = 4*20 + 5*60 = 380

This is lower than 400, so it is not a possible solution.

50 minutes walking, 50 minutes basketball

This means that w = 50, b = 50. So

4w + 5b = 4*50 + 5*50 = 450

This is between 400 and 600 calories, so it applies.

60 minutes walking, 80 minutes basketball

This means that w = 60, b = 80. So

4w + 5b = 4*60 + 5*80 = 640

This is higher than 600, so it is not a possible solution.

70 minutes walking, 60 minutes basketball

This means that w = 70, b = 60. So

4w + 5b = 4*70 + 5*60 = 580

This is between 400 and 600 calories, so it applies.