1.Idnia works at Euclid’s Electronics. She is paid a salary of $200 per week plus a commission of 5% of her sales during the week.
Idnia is offered another job at Fermat's Footwear, where the pay is a salary of $100 per week and 10% commission on all sales. She asks
you to help her determine which job she should keep.
Create a linear system that represents the two options. Label the equations 1 and 2 ( /2TH)
Graph the equations ( 5/COMM)
State the method of graphing you will use _______________________( /1 COMM)
c) Analyze the graph and complete the questions below. ( /8APP)
i. Where the two lines cross is called the point on intersection, or the solution to the system. At what coordinates do the two lines cross?
ii. What does this coordinate represent in terms of Idnia's sales, and pay for the
week?
iii. If Idnia usually makes $1500 worth of sales per week, which job should she take? Explain.
iv. Explain how does the graph help Idnia determine which is the better job?
v. What does the point (1000, 250) represent on the graph
You are on your own for all that ( /2TH) and ( 5/COMM) stuff
Your 2 equations are:
Euclid's pay = 200 + .05s
Fermat's pay = 100 + .1s , where s is sales for each part
so graph
y1 = 200 + .05x
y2 = 100 +.1x
copy and paste into a new window:
www.wolframalpha.com/input/?i=graph+y+%3D+200+%2B+.05x%2C+y+%3D+100%2B.1x+from+1000+to+2500
take it from here
0.05x-0.05x+0.10x+200+100
0.10x+300
To create a linear system that represents the two job options, we need to consider the salary and commission for each job.
Let x represent the amount of sales in dollars.
For the job at Euclid's Electronics:
Salary = $200 per week
Commission = 5% of sales
So the equation representing this job option is:
1. Salary + Commission = $200 + 0.05x
For the job at Fermat's Footwear:
Salary = $100 per week
Commission = 10% of sales
So the equation representing this job option is:
2. Salary + Commission = $100 + 0.1x
To graph the equations, we can use the slope-intercept form y = mx + b, where y represents the total pay and x represents the sales amount.
For equation 1:
y = 0.05x + 200
For equation 2:
y = 0.1x + 100
To graph these equations, you can plot a few points for each equation and then connect them with lines. Alternatively, you can convert the equations to slope-intercept form and identify the slope and y-intercept to plot the lines directly.
The method of graphing will be using the slope-intercept form to plot the lines directly.
c) Analyzing the graph:
i. The coordinates where the two lines cross represent the solution to the system, or the point of intersection. To find these coordinates, we can set the two equations equal to each other and solve for x and y:
0.05x + 200 = 0.1x + 100
0.05x - 0.1x = 100 - 200
-0.05x = -100
x = 2000
Substituting x = 2000 into either equation, we can solve for y:
y = 0.05(2000) + 200
y = 100 + 200
y = 300
So the coordinates where the two lines cross are (2000, 300).
ii. The coordinates (2000, 300) represent Idnia's sales of $2000 and her pay for the week of $300.
iii. If Idnia usually makes $1500 worth of sales per week, we can substitute x = 1500 into both equations and compare the y-values:
For equation 1: y = 0.05(1500) + 200 = 275
For equation 2: y = 0.1(1500) + 100 = 250
Based on these calculations, for sales of $1500 per week, Idnia would earn $275 at Euclid's Electronics (equation 1) and $250 at Fermat's Footwear (equation 2). Therefore, she should choose the job at Euclid's Electronics as it offers a higher pay.
iv. The graph helps Idnia determine which job is better by visually showing the points where the lines intersect. The point of intersection represents the sales amount and pay that would make both job options equally attractive. By comparing the pay for different sales amounts on the graph, Idnia can see which job offers a higher pay for her desired sales range.
v. The point (1000, 250) represents a sales amount of $1000 and a pay of $250.