How am I supposed to solve and graph this?
"Linda works at a pharmacy for $15 an hour. She also babysits for $10 an hour. Linda needs to earn at least $90 per week, but she does not want to work more than 20 hours per week. Show and describe the number of hours Linda could work at each job to meet her goals. List two possible solutions."
15p + 10b >= 90
p+b <= 20
6 hrs at pharmacy = $90
9 hrs babysitting = $90
2 hrs at pharmacy = 3 hrs babysitting
so, I think you can probably come up with other solutions.
How am I supposed to graph it?
just graph the two lines as equations.
Then, shade the region above the first, and below the 2nd.
To check your answer, click here:
http://www.wolframalpha.com/input/?i=solve+15p+%2B+10b+%3E%3D+90%2C+p%2Bb+%3C%3D+20
To solve this problem, we can set up a system of inequalities to represent Linda's situation. Let's denote the number of hours she works at the pharmacy by 'x' and the number of hours she babysits by 'y.'
First, let's write down the constraints or conditions given in the problem:
1. Linda needs to earn at least $90 per week.
2. Linda does not want to work more than 20 hours per week.
Now, we can translate these constraints into mathematical inequalities:
1. The total earnings per week should be at least $90:
15x + 10y ≥ 90
2. The total number of hours worked per week should not exceed 20:
x + y ≤ 20
Now we can graph these inequalities on a coordinate plane to visualize the possible solutions.
To graph the first inequality (15x + 10y ≥ 90):
1. Convert the inequality to an equation by replacing the ≥ symbol with =:
15x + 10y = 90
2. Solve the equation for y:
y = (90 - 15x)/10
3. Choose some values for x and calculate the corresponding y-values:
For example:
Let x = 0, then y = (90 - 15*0)/10 = 9
Let x = 6, then y = (90 - 15*6)/10 = 3
4. Plot the points on the graph and connect them to form a line.
To graph the second inequality (x + y ≤ 20):
1. Convert the inequality to an equation by replacing the ≤ symbol with =:
x + y = 20
2. Choose some values for x and calculate the corresponding y-values:
For example:
Let x = 0, then y = 20
Let x = 10, then y = 10
3. Plot the points on the graph and connect them to form a line.
The shaded area that satisfies both inequalities represents the valid solutions. Any point within or on the boundary of this shaded region will fulfill Linda's goals.
Two possible solutions could be:
1. (x = 6, y = 3) - This means Linda works 6 hours at the pharmacy and 3 hours babysitting. Her total earnings would be $90.
2. (x = 10, y = 10) - This means Linda works 10 hours at the pharmacy and 10 hours babysitting. Her total earnings would be $250.
Note: There can be infinitely many possible solutions within the shaded region, depending on the specific values chosen for x and y within the valid range.