Sales clerk at an appliance store have a chance of 2 payment:
Plan A: $580 every 2 weeks plus 4.2 % commission on all sales
Plan B: $880 every 2 weeks plus 1.2 % commission on all sales
a) Write a linear system to model this situation
b) Graph the linear system in part a
c) Use the graph to solve this problem: What must the sales for a 2-week period be for a clerk to receive the same salary with both plans?
incomeA = 580 + .042x , where x is total sales
incomeB = 880 + .012x
to sketch it, you obviously have to scale the x-axis and the income axis
a) To model this situation, we can write a linear system with two equations:
Let's denote the weekly sales as S, and the total salary in a 2-week period for Plan A and Plan B as A and B, respectively. The equations can be written as:
Plan A: A = 580 + 0.042S
Plan B: B = 880 + 0.012S
b) To graph the linear system, we need to plot the two equations on a graph.
Plan A equation: A = 580 + 0.042S
Plan B equation: B = 880 + 0.012S
On the graph, we can mark the x-axis as S (sales) and the y-axis as A (salary).
To plot the Plan A equation:
- Set S = 0, calculate A. This gives us the y-intercept.
- Choose any other value for S. Calculate A, and plot the point (S, A).
To plot the Plan B equation:
- Set S = 0, calculate B. This gives us the y-intercept.
- Choose any other value for S. Calculate B, and plot the point (S, B).
Now we have two points for each plan. Connect them to form the respective lines.
c) To solve the problem using the graph, look for the point where the two lines intersect. This represents the sales amount (S) for a 2-week period where the salary is the same for both plans.
At the point of intersection, the A value (salary for Plan A) is equal to the B value (salary for Plan B).