Respuesta :
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 [tex]125x[/tex].
The spa charges $250 for a pedicure + 90-minute massage package, so amount earned from y pedicure + 90-minute massages will be [tex]250y[/tex].
We have been given that one day the spa had 27 customers. We can represent this information in an equation as:
[tex]x+y=27...(1)[/tex]
[tex]y=27-x...(1)[/tex]
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:
[tex]125x+250y=5250...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]125x+250(27-x)=5250[/tex]
Let us solve for x.
[tex]125x+6750-250x=5250[/tex]
[tex]-125x+6750=5250[/tex]
[tex]-125x+6750-6750=5250-6750[/tex]
[tex]-125x=-1500[/tex]
[tex]\frac{-125x}{-125}=\frac{-1500}{-125}[/tex]
[tex]x=12[/tex]
Upon substituting [tex]x=12[/tex] in equation (1), we will get:
[tex]y=27-12=15[/tex]
Therefore, the spa performed 12 one hour massages and 15 pedicure + 90-minute massage packages that is [tex](12,15)[/tex].
