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 ≥ 4004w + 5b ≤ 600Which are possible solutions for the number of minutes Joshua can participate in each activity? Check all that apply.a. 40 minutes walking, 40 minutes basketballb. 60 minutes walking, 20 minutes basketballc. 20 minutes walking, 60 minutes basketballd. 50 minutes walking, 50 minutes basketballe. 60 minutes walking, 80 minutes basketballf. 70 minutes walking, 60 minutes basketball

Answer 1

Options D and F are possible

Explanation:

Let w represent walking

Let b represent basketball

The given inequalities are

4w + 5b ≥ 400 ........(1)

4w + 5b ≤ 600 .........(2)

Substitute each options in the inequalities to get the possible solution

For the first option,

w = 40 minutes walking

b = 40 minutes basketball

So we have

4(40) + 5(40) ≥ 400

160 + 200 ≥ 400

360 ≥ 400

4(40) + 5(40) ≤ 600

360 ≤ 600

Option A is not possible

For option B

w = 60 minutes walking

b = 20 minutes basketball

So we have

4(60) + 5(20) ≥ 400

240 + 100 ≥ 400

340 ≥ 400

4(60) + 5(20) ≤ 600

340 ≤ 600

This is also not possible

For option C

w = 20 minutes walking

b = 60 minutes basketball

So we have

4(20) + 5(60) ≥ 400

80 + 300 ≥ 400

380 ≥ 400

4(20) + 5(60) ≤ 600

380 ≤ 600

Option C is not possible

For option D

w = 50 minutes walking

b = 50 minutes basketball

So we have

4(50) + 5(50) ≥ 400

200 + 250 ≥ 400

450 ≥ 400

4(50) + 5(50) ≤ 600

450 ≤ 600

Option D is possible

For option E

w = 60 minutes walking

b = 80 minutes basketball

So we have

4(60) + 5(80) ≥ 400

240 + 400 ≥ 400

640 ≥ 400

4(60) + 5(80) ≤ 600

640 ≤ 600

Option E is not possible

For option F

w = 70 minutes walking

b = 60 minutes basketball

So we have

4(70) + 5(60) ≥ 400

280 + 300 ≥ 400

580 ≥ 400

4(70) + 5(60) ≤ 600

580 ≤ 600

Option F is also possible

Therefore options D and F are the possible solutions for the number of minutes Joshua can use in taking part in each activity