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: 50 minutes walking; 50 minutes basketball
F: 70 minutes walking; 60 minutes basketball

Answer 2

Answer:

Given the inequalities:

$4w+5b\geq 400$               .....[1]

$4w+5b\leq 600$               .....[2]

where w is the walking and b is the basketball

To get the possible solution we substitute each options in above inequalities to satisfy the equation;

Option A:

w = 40 minutes walking,  b = 40 minutes basketball.

Substitute in [1] we have;

$4 \times 40 + 5 \times 40 \geq 400$

$160+200 \geq 400$

$320 \geq 400$  

Substitute in [2] we have;

$4(40) + 5(40) \leq 600$

$320 \leq 600$

Option A is not possible because the solution 40 minutes walking, 40 minutes basketball does not satisfy equation [1].

Option B:

Similarly, for 60 minutes walking, 20 minutes basketball

Option B is not possible because the solution 60 minutes walking, 20 minutes basketball does not satisfy equation [1].

Option C:

for 20 minutes walking, 60 minutes basketball

Option C is not possible because the solution 20 minutes walking, 60 minutes basketball does not satisfy equation [1].

Option D:

For 50 minutes walking, 50 minutes basketball.

Substitute in [1] we have;

$4 \times 50+ 5 \times 50\geq 400$

$200+250 \geq 400$

$450 \geq 400$  

Substitute in [2] we have;

$4(50) + 5(50) \leq 600$

$450 \leq 600$

Option D is  possible because the solution 50 minutes walking, 50 minutes basketball does satisfy the inequality equation [1] and [2].

Option E:

Similarly, for 60 minutes walking, 80 minutes basketball

Option E is not possible because the solution 60 minutes walking, 80 minutes basketball does not satisfy inequality equation [2].

Option F:

For 70 minutes walking, 60 minutes basketball.

Substitute in [1] we have;

$4 \times 70+ 5 \times 60\geq 400$

$280+300 \geq 400$

$580\geq 400$  

Substitute in [2] we have;

$4(70) + 5(60) \leq 600$

$580\leq 600$

Option F is  possible because the solution 70 minutes walking, 60 minutes basketball does satisfy the inequality equation [1] and [2].

Therefore, only options D and F are the possible solutions for the number of minutes Joshua can participate in each activity.