Question

DeAndre the trainer has two solo workout plans, Plan A and Plan B. On Friday, 3 clients did Plan A and 2 did Plan B. On Saturday, a clients did Plan A and 4 did Plan B. DeAndre trained his Friday clients for a total of 7 hours and his Saturday clients for a total of 17 hours. How long does each of the workout plans last?

a) Plan A: 2 hours, Plan B: 3 hours
b) Plan A: 3 hours, Plan B: 2 hours
c) Plan A: 4 hours, Plan B: 5 hours
d) Plan A: 5 hours, Plan B: 4 hours

Answer 1

The duration of Plan A is 0 hours and the duration of Plan B is 4 hours.

Step-by-step explanation:

To find the durations of Plan A and Plan B, we need to set up a system of equations using the information given. Let's represent the duration of Plan A as 'x' and the duration of Plan B as 'y'. From the given information:

3x + 2y = 7 (equation 1)

x + 4y = 17 (equation 2)

We can solve this system of equations using any method of our choice. For this example, let's use the substitution method:

From equation 1, we can express x in terms of y:

x = (7 - 2y) / 3

Substituting this value for x in equation 2, we can solve for y:

(7 - 2y) / 3 + 4y = 17

Simplifying this equation further, we get:

7 - 2y + 12y = 51

Combining like terms, we have:

10y = 44

Dividing both sides by 10, we find:

y = 4

Substituting this value for y in equation 1, we can solve for x:

3x + 2(4) = 7

3x + 8 = 7

3x = -1

Dividing both sides by 3, we find:

x = -1/3

Since the duration of a workout plan cannot be negative, we can conclude that:

Plan A: 0 hours

Plan B: 4 hours