I need the inequality equations,

Question

You have at most 28 minutes to work out. Jogging on the treadmill burns 35 calories per minute, and lifting weights burn 30 calories per minute. You need to burn at least 800 calories during your workout.

 

a. Define the variables. 

 

b. Write a system of linear inequalities that represents this situation. 

 

 

c. Is it possible to jog for 12 minutes and lift weights for 14 minutes in this situation? Justify your answer. 

Answer 1

J = minutes Jogging

L = minutes lifting weights

Since we know that you have to work out no more than 28 minutes. First inequality has to focus on minutes.

J + L ≤ 28 ----- minutes running and minutes lifting can't be more than 28 minutes

We know that we want to burn at least 800 calories. So second inequality has to focus on calories.

35J + 30L ≥ 800 --- calories burned running and lifting have to me more than 800.

To determine if 12 and 14 minutes jogging and lifting respectively is possible you must substitute in each inequality to see if it makes that true.

12 + 14 ≤ 28..... yes 26 is less than 28.

35(12) + 30(14) ≥ 800

420 + 420 ≥ 800.... yes 820 is larger than 800.

Therefore yes jogging for 12 minutes and lifting for 14 minutes would satisfy the situation.