Question

URGENT!!! 100 POINTS WILL GIVE BRAINLIEST, PLEASE DONT JUST PUT SOMETHING FOR POINTS a nail salon is looking to open a new location. The rent at Location A is $1200 per month and they will charge $45 per manicure/pedicure. The rent at Location B is $1800 per month and they will charge $60 per manicure/pedicure. How many manicure/pedicure will they need to do to make the same profit at each location?
a. Write a let-statement defining your variable.

b. Write an equation in one variable to solve.

c. Show work to solve the equation.

d. Write a sentence for your final answer.​

Answer 1

Answer:

$\textsf{a) \quad Let x be the number of manicure/pedicures per month}.$

$\textsf{b)} \quad 60x-1800=45x-1200$

$\textsf{c) \quad x=40 }$

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:

$\boxed{y = 45x - 1200}$

Location B

The rent at Location B is $1800 per month and they will charge $60 per manicure/pedicure:

$\boxed{y = 60x - 1800}$

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:

$\boxed{60x-1800=45x-1200}$

Part (c)

Solve the equation from part (b):

$\implies 60x-1800=45x-1200$

$\implies 60x-1800-45x=45x-1200-45x$

$\implies 15x-1800=-1200$

$\implies 15x-1800+1800=-1200+1800$

$\implies 15x=600$

$\implies 15x\div 15=600 \div 15$

$\implies x=40$

Part (d)

The two salons will need to do 40 manicures/pedicures each month to make the same profit at each location.