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

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!