Let A be the augmented matrix of a linear system. Find the solution for this
linear system.
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Let x represent number of massages and y represent number of pedicure + 90-minute massage packages.

We have been given that a spa charges $125 for a one hour massage, so amount earned from x massages would be .

The spa charges $250 for a pedicure + 90-minute massage package, so amount earned from y pedicure + 90-minute massages will be .

We have been given that one day the spa had 27 customers. We can represent this information in an equation as:

Since spa made $5,250, so amount earned from both massages would be equal to 5,250. We can represent this information in an equation as:

Upon substituting equation (1) in equation (2), we will get:

Let us solve for x.

Upon substituting  in equation (1), we will get:

Therefore, the spa performed 12 one hour massages and 15 pedicure + 90-minute massage  packages that is .