precal word problrms

Question

Miguel the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 

3

 clients who did Plan A and 

8

 who did Plan B. On Saturday there were 

5

 clients who did Plan A and 

2

 who did Plan B. Miguel trained his Friday clients for a total of 

15

 hours and his Saturday clients for a total of 

8

 hours. How long does each of the workout plans last?

Answer 1

3A + 8B = 15

5A + 2B = 8

Can you solve the system and answer?

Answer 2

Let's define a variable A as the hours that a single plan A session lasts, and variable B as the hours that a single plan B session lasts.

On Friday, 3 clients did plan A and 8 did plan B, totaling 15 hours.

From this, we can make an equation: 3A + 8B = 15

On Saturday, 5 clients did plan A and 2 did plan B, totaling 8 hours.

From this, we can make another equation: 5A + 2B = 8

We now have a system of equations that we can use to solve for A and B:

i) 3A + 8B = 15

ii) 5A + 2B = 8

Rewriting equation ii , we can get 2B = 8 - 5A

Multiplying it by 4 on both sides, we get 8B = 32 - 20A

We can now use this expression to replace the 8B term inside equation i

Equation i modified with the replaced term:

3A + (32 - 20A) = 15

Now we can solve for A

32 - 17A = 15

-17A = -17

A = 1

Now we know that A = 1 hour

We can plug this value of A back into any equation to solve for B. I'll plug it into equation ii:

5(1) + 2B = 8

5 + 2B = 8

2B = 8 - 5

2B = 3

B = 3/2

B = 1.5

Now we know that B = 1.5 hours

Answer: Plan A session = 1 hour, Plan B session = 1.5 hours