Question

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

pedicure + 90-minute massage package. One day, the spa had
27 customers and made $5,250.
How many massages, x, and pedicure + 90-minute massage
packages, y, did the spa perform? Express your answer as an
ordered pair (x,y).
Enter the answer

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`

`(-125x)/(-125)=(-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)`.