1. We can define the variables as follows:
- Let j = the number of minutes spent jogging on the treadmill.
- Let w = the number of minutes spent lifting weights.
2. 2) We can write the following system of linear inequalities to represent the situation:
35j + 30w ≥ 755
j + w ≤26
j ≥ 0
w ≥ 0
3. The graph for the linear inequalities start with the boundary line for the first inequality, which is 35j + 30w = 755, simplified to 7j + 6w = 151.
The boundary line for the second inequality is j + w = 26. We can graph these two lines and shade the region that satisfies all four inequalities. The shaded region will be a polygon with vertices at (0, 0), (0, 26), (11, 15), and (22, 4).
How the variables, linear inequalities, and graph are developed:
The total time in minutes available to work out ≤ 26 minutes
The number of calories Jogging burns per minute = 35
The number of calories lifting weight burns per minute = 30
The least number of calories you need to burn during the workout = 755
1) The variables are:
Let j = the number of minutes spent jogging on the treadmill.
Let w = the number of minutes spent lifting weights.
2) Linear Inequalities:
Inequality 1: 35j + 30w ≥ 755 (to represent the minimum number of calories that need to be burned during the workout.)
Inequality 2: j + w ≤26 (to represent the maximum amount of time available for the workout.)
Inequality 3: j ≥ 0
Inequality 4: w ≥ 0
Inequalities 3 and 4 show that the number of minutes spent jogging and lifting weights cannot be negative.
4) Graph:
To graph the system of linear inequalities, we can start by graphing the boundary lines of the inequalities.
Thus, we can conclude that one can jog for 11 minutes and lift weights for 14 minutes in this situation, since (11, 14) fall inside the shaded region.