Question

Claudia works part-time at a nail salon. She earns $5 for each manicure and $15 for

each pedicure. Last week she had 40 customers and earned a total of $300. How
many customers had manicures and how many had pedicures. (Do not forget to
include the let statements)

Answer 1

Claudia performed 30 manicures and 10 pedicures last week. We found this by setting up a system of two equations with two variables, representing the number of manicures and pedicures, and then solving the system of equations.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's use the variable 'm' for the number of manicures and 'p' for the number of pedicures. From the problem, we know that Claudia earns $5 for each manicure and $15 for each pedicure. We also know that she had a total of 40 customers and earned a total of $300.

We can now set up the following two equations:

m + p = 40 (equation 1)

5m + 15p = 300 (equation 2)

To solve this system, we can use substitution or elimination. Let's use elimination:

Multiplying equation 1 by 5, we get:

5m + 5p = 200 (equation 3)

Now, we can subtract equation 3 from equation 2:

(5m + 15p) - (5m + 5p) = 300 - 200

Simplifying, we have:

10p = 100

Dividing by 10, we find:

p = 10

Substituting this value back into equation 1, we get:

m + 10 = 40

Solving for m, we have:

m = 30

Therefore, Claudia had 30 manicures and 10 pedicures.