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 geq 400
4w + 5b leq 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

Explanation:

Step1: Check 40,40

Calculate \(4(40)+5(40)=160 + 200 = 360\). Since \(360<400\), it doesn't satisfy \(4w + 5b\geq400\).

Step2: Check 60,20

Calculate \(4(60)+5(20)=240+100 = 340\). Since \(340<400\), it doesn't satisfy \(4w + 5b\geq400\).

Step3: Check 20,60

Calculate \(4(20)+5(60)=80 + 300 = 380\). Since \(380<400\), it doesn't satisfy \(4w + 5b\geq400\).

Step4: Check 50,50

Calculate \(4(50)+5(50)=200+250 = 450\). Since \(400\leq450\leq600\), it satisfies both inequalities.

Step5: Check 60,80

Calculate \(4(60)+5(80)=240 + 400 = 640\). Since \(640>600\), it doesn't satisfy \(4w + 5b\leq600\).

Step6: Check 70,60

Calculate \(4(70)+5(60)=280+300 = 580\). Since \(400\leq580\leq600\), it satisfies both inequalities.

Answer:

• 50 minutes walking, 50 minutes basketball
• 70 minutes walking, 60 minutes basketball