The relationship described below can be modeled using an equation.
Identify the variables and write an equation to solve the questions below. Number of subscriptions sold/ pay per wk
5 150
10 200
15 250
20 300
25 350
Sheryl has a part-time job working for a large company selling magazine subscriptions. Above is the pay scale she was given to calculate her weekly pay checks.
(a) Write an equation to calculate the pay per week given the number of subscriptions sold.
(b) What is her weekly pay if she sells 40 subscriptions?
To model the relationship between the number of subscriptions sold and the pay per week, we can use a linear equation in the form of y = mx + b, where y represents the pay per week, x represents the number of subscriptions sold, m represents the slope or rate of change, and b represents the y-intercept.
We can first find the value of m by calculating the rate of change between any two points. Let's choose the points (15, 250) and (20, 300):
m = (300 - 250) / (20 - 15)
m = 50 / 5
m = 10
Now that we have the value of m, we can substitute it into the equation as:
y = 10x + b
To find the value of b, we can substitute the known values of x and y from any given point in the equation. Let's use the point (5, 150):
150 = 10(5) + b
150 = 50 + b
b = 150 - 50
b = 100
So the equation to calculate the pay per week is:
y = 10x + 100
Now, to determine Sheryl's weekly pay if she sells 40 subscriptions, we can substitute x = 40 into the equation:
y = 10(40) + 100
y = 400 + 100
y = 500
Therefore, Sheryl's weekly pay if she sells 40 subscriptions would be $500.