Questions: Carmen the trainer offers two solo workout plans: Plan A and Plan B. Each client does either one or the other (not both). Carmen trained on Monday and Tuesday last week. The table below shows the number of Plan A and Plan B clients Carmen trained each day and the total time (in hours) she trained. - Monday and Tuesday: - Number of Plan A workouts: 9 on Monday, 3 on Tuesday - Number of Plan B workouts: 7 on Monday, 5 on Tuesday - Total time (In hours): 12 on Monday, 6 on Tuesday Let x be the length (in hours) of each Plan A workout. Let y be the length (in hours) of each Plan B workout. (a) Write a system of equations that could be used to find the length (in hours) of each type of workout. (b) How long (in hours) was each type of workout? Length of each Plan A workout: square hours Length of each Plan B workout: square hours

Carmen the trainer offers two solo workout plans: Plan A and Plan B. Each client does either one or the other (not both). Carmen trained on Monday and Tuesday last week. The table below shows the number of Plan A and Plan B clients Carmen trained each day and the total time (in hours) she trained.

- Monday and Tuesday:
- Number of Plan A workouts: 9 on Monday, 3 on Tuesday
- Number of Plan B workouts: 7 on Monday, 5 on Tuesday
- Total time (In hours): 12 on Monday, 6 on Tuesday

Let x be the length (in hours) of each Plan A workout. Let y be the length (in hours) of each Plan B workout.
(a) Write a system of equations that could be used to find the length (in hours) of each type of workout.

(b) How long (in hours) was each type of workout?

Length of each Plan A workout: square hours

Length of each Plan B workout: square hours

Transcript text: Carmen the trainer offers two solo workout plans: Plan A and Plan B. Each client does either one or the other (not both). Carmen trained on Monday and Tuesday last week. The table below shows the number of Plan A and Plan B clients Carmen trained each day and the total time (in hours) she trained. \begin{tabular}{|c|c|c|} \hline & Monday & Tuesday \\ \hline \begin{tabular}{c} Number of \\ Plan A workouts \end{tabular} & 9 & 3 \\ \hline \begin{tabular}{c} Number of \\ Plan B workouts \end{tabular} & 7 & 5 \\ \hline \begin{tabular}{c} Total time \\ (In hours) \end{tabular} & 12 & 6 \\ \hline \end{tabular} Let $x$ be the length (in hours) of each Plan $A$ workout. Let $y$ be the length (in hours) of each Plan $B$ workout. (a) Write a system of equations that could be used to find the length (in hours) of each type of workout. (b) How long (in hours) was each type of workout? Length of each Plan $A$ workout: $\square$ hours Length of each Plan $B$ workout: $\square$ hours

Solution

Solution Steps

To solve this problem, we need to set up a system of linear equations based on the given data. We will use the number of Plan A and Plan B workouts and the total time spent training on each day to form these equations. Then, we will solve the system of equations to find the length of each type of workout.

Define variables $ x $ and $ y $ for the length of Plan A and Plan B workouts, respectively.
Use the data from Monday and Tuesday to form two equations.
Solve the system of equations using Python.

Step 1: Formulate the System of Equations

Let $ x $ be the length (in hours) of each Plan A workout and $ y $ be the length (in hours) of each Plan B workout. Based on the data provided:

For Monday: \[ 9x + 7y = 12 \]

For Tuesday: \[ 3x + 5y = 6 \]

Step 2: Solve the System of Equations

We can represent the system of equations in matrix form as follows: \[ A = \begin{bmatrix} 9 & 7 \\ 3 & 5 \end{bmatrix}, \quad B = \begin{bmatrix} 12 \\ 6 \end{bmatrix} \] By solving this system, we find: \[ x \approx 0.75, \quad y \approx 0.75 \]

Step 3: Interpret the Results

The solution indicates that the length of each type of workout is: \[ \text{Length of each Plan A workout: } x \approx 0.75 \text{ hours} \] \[ \text{Length of each Plan B workout: } y \approx 0.75 \text{ hours} \]