System of Equations Word Problems

Question

Maya 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 5 clients who did Plan A and 6 who did Plan B. On Saturday there were 3 clients who did Plan A and 2 who did Plan B. Maya trained her Friday clients for a total of 7 hours and her Saturday clients for a total of 3 hours. How long does each of the workout plans last?

Answer 1

Here's the setup:

For Friday: 5A + 6B = 7 hrs

For Saturday: 3A + 2B = 3 hrs

Since the 6 is a multiple of 2, I suggest you use the elimination method and remove the B terms:

5A + 6B = 7

-3(3A + 2B = 3) Do the multiplication as shown on both sides of the eqn.

Now you can add. Once you've solved for A, substitute it in one of the original equations and solve for B, then check your results.

Hint: Both A & B are fractions of an hour.

P.S. There are plenty of similar system of equations examples in the Wyzant Ask An Expert archives for you to study.

Answer 2

Hello Crystal the Math Person,

One way to think about this is that Maya has 5 A clients and 6 B clients on Friday and worked 7 hours.

That can be written as the equation 5A + 6B = 7

On Saturday she had 3 A clients and 2 B clients and worked 3 hours.

That can be written as the equation 3A + 2B = 3

The two equations together make the system:

5A + 6B = 7

3A + 2B = 3

If you choose the elimination method to solve this, multiplying the bottom equation by -3 is helpful

5A + 6B = 7

-9A - 6B = -9

Adding these two equations together:

-4A = -2 then dividing by -4

A = 1/2

Using A = 1/2 to substitute into one of the original equations:

5(1/2) + 6B = 7

2.5 + 6B = 7 Then subtract 2.5

6B = 4.5 Then divide by 6

B = 4.5/6 = .75 = 3/4

Plan A is a 30 minute workout, Plan B is a 45 minute workout.

Happy Monday