Question

Lisa gives child(x) and adult(y) haircuts in her salon. She charges $10 for a child and $40 for an adult haircut. Her goal is to make at least $1000 per week and work no more than 40 hours. The shaded region of the graph represents the possible combinations of adult and child haircuts that will allow her to meet her goal. If Lisa gives 60 child haircuts she must give _____ adult haircuts to meet her goal

Answer 1

Answer: The solution is 10 adult haircuts. Since Lisa charges $10 for a child she will make $600 and it will take 30 hours. this give her 10 more hours of working time for the week and she must take $400 to meet her $1000 goal.To do this she must give 10 adult haircuts.

Answer 2

Hey, first time answering! Hope I do things justice!

This one luckily can be done without use of a graph, since we have all of the information we need right in the problem itself. We already have our variables identified, and their coefficients declared.
The equation we're filling in is Ax +By = C since we know that X and Y are going to have values of person getting hair cut (x or y) and the number of dollars they are paying to get their hair cut (A and B).
x = children,
1000 = 10x + 40y We already know what X is in this equation.
1000 = 10(60) + 40y So we just replace X with the number of children.
1000= 600 + 40y Calculating 10*60=600
1000-600= 40y Then to get Y on its ow
400 = 40y
10=y
So 10 adults.
This is a simple linear problem that can be expressed as
y=mx+b
or
Ax+By=C
or
\[y-y_1=m(x-x_1) \] where \[m=(x_2-x_1)/(y_2-y_1) \]
My old high school mathematics teacher always said that it's important to have multiple tools in your toolbox. The individual who can tackle a problem at different angles is more likely to achieve success.

Answer 3

Also, the number of hours is not used in this equation. Since it doesn't say how long each haircut takes, or how many hours she has worked, there is no need to consider this.