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Sagot :
Answer:
[tex]\textsf{a) \quad Let $x$ be the number of manicure/pedicures per month}.[/tex]
[tex]\textsf{b)} \quad 60x-1800=45x-1200[/tex]
[tex]\textsf{c) \quad $x=40$}[/tex]
d) The two salons will need to do 40 manicures/pedicures each month to make the same profit at each location per month.
Step-by-step explanation:
Part (a)
Definition of the variables:
- Let x be the number of manicure/pedicures per month.
- Let y be the total profit (n dollars).
Part (b)
Create an equation for each location.
Location A
The rent at Location A is $1200 per month and they will charge $45 per manicure/pedicure:
[tex]\boxed{y = 45x - 1200}[/tex]
Location B
The rent at Location B is $1800 per month and they will charge $60 per manicure/pedicure:
[tex]\boxed{y = 60x - 1800}[/tex]
To determine the number of treatments the two salons will need to give to make the same profit at each location, substitute the second equation into the first equation:
[tex]\boxed{60x-1800=45x-1200}[/tex]
Part (c)
Solve the equation from part (b):
[tex]\implies 60x-1800=45x-1200[/tex]
[tex]\implies 60x-1800-45x=45x-1200-45x[/tex]
[tex]\implies 15x-1800=-1200[/tex]
[tex]\implies 15x-1800+1800=-1200+1800[/tex]
[tex]\implies 15x=600[/tex]
[tex]\implies 15x\div 15=600 \div 15[/tex]
[tex]\implies x=40[/tex]
Part (d)
The two salons will need to do 40 manicures/pedicures each month to make the same profit at each location.
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