Question

A spa charges $125 for a one hour massage and $250 for a

Answer 1

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 $125x$.

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

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

$x+y=27...(1)$

$y=27-x...(1)$

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:

$125x+250y=5250...(2)$

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

$125x+250(27-x)=5250$

Let us solve for x.

$125x+6750-250x=5250$

$-125x+6750=5250$

$-125x+6750-6750=5250-6750$

$-125x=-1500$

$\frac{-125x}{-125}=\frac{-1500}{-125}$

$x=12$

Upon substituting $x=12$ in equation (1), we will get:

$y=27-12=15$

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