Elsa the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 4 clients who did Plan A and 8 who did Plan B. On Saturday there were 2 clients who did Plan A and 3 who did Plan B. Elsa trained her Friday clients for a total of 9 hours and her Saturday clients for a total of 4 hours. How long does each of the workout plans last?

plan A lasts for 1.25 hours.

Plan B lasts for 0.5 hour.

Step-by-step explanation:

Let x represent the number of hours that plan A lasts.

Let y represent the number of hours that plan B lasts.

On Friday there were 4 clients who did Plan A and 8 who did Plan B. Elsa trained her Friday clients for a total of 9 hours. This means that

4x + 8y = 9 - - - - - - - - - - - - -1

On Saturday there were 2 clients who did Plan A and 3 who did Plan B. Elsa trained her Saturday clients for a total of 4 hours. This means that

2x + 3y = 4 - - - - - - - - - - - 2

Multiplying equation 1 by 1 and equation 2 by 2, it becomes

4x + 8y = 9

4x + 6y = 8

Subtracting, it becomes

2y = 1

y = 1/2 = 0.5

Substituting y = 0.5 into equation 1, it becomes

4x + 8 × 0.5 = 9

4x + 4 = 9

4x = 9 - 4 = 5

x = 5/4

x = 1.25

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1