suppose you can work a total of no more than 20 hours per week at your two jobs. Babysitting pays $5 per hour, and your cashier job pays $6 per hour. youneed to earn at least $90per week to cover your expenses. Write a system of inequalities that show s the various numbers of hours youcan work at each job. Graph the result.
you mow your neighbor's lawn in 5 hours and earn 45$, what is your hourly wage?
Let's define the following variables:
x = number of hours worked babysitting
y = number of hours worked as a cashier
Based on the given information, we can construct the following system of inequalities:
1. Total hours worked per week: x + y ≤ 20 (since you cannot work more than 20 hours per week)
2. Amount earned through babysitting: 5x
3. Amount earned through cashier job: 6y
4. Total amount earned per week: 5x + 6y ≥ 90 (since you need to earn at least $90 per week)
Now, we can graph these inequalities on a coordinate plane.
Let's first graph the total hours worked per week inequality (x + y ≤ 20):
To graph this line, we can start by drawing the line x + y = 20, which passes through the points (20, 0) and (0, 20). Then, we need to shade the region below this line to represent the condition x + y ≤ 20.
Next, let's graph the total amount earned per week inequality (5x + 6y ≥ 90):
To graph this line, we can start by drawing the line 5x + 6y = 90, which passes through the points (9, 10) and (18, 0). Then, we need to shade the region above this line to represent the condition 5x + 6y ≥ 90.
The resulting graph will show the feasible solution region, where both conditions are satisfied. The shaded area below the first line (x + y ≤ 20) and above the second line (5x + 6y ≥ 90) will represent the different combinations of hours you can work at each job to earn at least $90 per week while not exceeding a total of 20 hours.
Note: Since I am an AI text-based bot, I cannot draw a graph directly for you. However, you can use online graphing tools or software, such as Desmos, GeoGebra, or even Excel, to graph the equations and inequalities.
To write a system of inequalities and graph the result, we need to define the variables and set up the constraints based on the given information.
Let's use the variables:
x: number of hours worked as a babysitter per week.
y: number of hours worked as a cashier per week.
Now let's set up the constraints based on the given information:
1. Total working hours constraint: The total number of hours worked per week cannot exceed 20 hours.
Therefore, the first constraint equation is:
x + y ≤ 20 -- (1)
2. Minimum earnings constraint: You need to earn at least $90 per week to cover your expenses.
The total earnings from babysitting (5x) and cashier job (6y) must be greater than or equal to $90.
The second constraint equation is:
5x + 6y ≥ 90 -- (2)
Now, let's graph the solution to these inequalities.
Step 1: Graph the total working hours constraint:
To do this, convert the inequality into the equation x + y = 20.
Plot the line x + y = 20 on the graph and shade the region below/along the line.
Step 2: Graph the minimum earnings constraint:
To do this, convert the inequality into the equation 5x + 6y = 90.
Plot the line 5x + 6y = 90 on the graph and shade the region above/along the line.
Step 3: Identify the feasible region:
The feasible region is the region where both constraints are satisfied. It is the region where the shaded areas of both inequalities overlap.
The graphed system of inequalities shows the various combinations of hours you can work at each job that satisfy the constraints.
Note: Due to the limitations of a text-based format, I am unable to provide a visual graph here. It's recommended to use graphing software or manually draw the graph on graph paper to visualize the solution.