Question

Jessica 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 Wednesday there were 5 clients who did Plan A and
who did Plan B. On Thursday there were
clients who did Plan A and 2 who did Plan B. Jessica trained her Wednesday clients for a total of 6 hours and her Thursday clients for a total of 7 hours. How long does each of the workout plans last?

Length of each PlanA workout: __ hours
Length of each Plan B worout: __ hours

Answer 1

Okay! So, first create a system of equations - let a be the duration of a Plan A session and b be the duration of a Plan B session

For Wednesday: 5a + 8b = 6 hours

For Thursday: 3a + 2b = 7 hours

You can use several methods but I'm going to use elimination!

Multiply the first equation by -4,and multiply the second equation by 1

−4(3a+2b=7)

1(5a+8b=6)

Becomes:

−12a−8b=−28

5a+8b=6

Then, add these two equations to eliminate b.

−7a=−22

Then solve−7a=−22 for a by dividing both sides by -7

a= 22/7 or 3.1 ( round 3.14285714 down)

Now that we've found a, let's plug it back in to solve for b.

Write down one of the original equations, I'm going to choose 3a+2b=7. Substitute 22/7 for a.

3(22/7)+2b=7

Solve from here, and you'll end up with b= -17/14 or -1.2 ( round -1.21428571 down)

So, again, a= 22/7 or 3.1 and b= -17/14 or -1.2

I hope this helps!

Answer 2

Okay! So, first create a system of equations - let a be the duration of a Plan A session and b be the duration of a Plan B session

For Wednesday: 5a + 8b = 6 hours

For Thursday: 3a + 2b = 7 hours

You can use several methods but I'm going to use elimination!

Multiply the first equation by -4,and multiply the second equation by 1

−4(3a+2b=7)

1(5a+8b=6)

Becomes:

−12a−8b=−28

5a+8b=6

Then, add these two equations to eliminate b.

−7a=−22

Then solve−7a=−22 for a by dividing both sides by -7

a= 22/7 or 3.1 ( round 3.14285714 down)

Now that we've found a, let's plug it back in to solve for b.

Write down one of the original equations, I'm going to choose 3a+2b=7. Substitute 22/7 for a.

3(22/7)+2b=7

Solve from here, and you'll end up with b= -17/14 or -1.2 ( round -1.21428571 down)

So, again, a= 22/7 or 3.1 and b= -17/14 or -1.2

I hope this helps!