Question

As a salesperson at Scrapbooks and

Treasures, Alysse receives a monthly
base pay plus commission on all that she
sells. If she sells $500 worth of
merchandise in one month, she is paid
$515. If she sells $900 of merchandise in
one month, she is paid $607.
Find Alysse's total salary function, s(x), when
she sells x dollars of merchandise.
s(x)=

Answer 1

s(x) = 0.23x + 400

Explanation:

Let x = cost of merchandise sold

We start by finding the slope which is the percent of commission Alysse receives.

Let's start with doing 607 - 515. This is because we are subtracting the commissions, which also can be y2 - y1. Then, we do 900-500=400 (x2-x1). This is how to find the slope of the function.
`(y2-y1)/(x2-x1)=(92)/(400) =0.23`, 0.23 being the slope.

s(x) = b+0.23x, now substitute values making the money received as s(x).

515 = b+0.23(500)

515=b+115

-115 -115

400 = b

607 = 400+0.23(900)

607 = 400 + 207

607 = 607

So, s(x) = 0.23x + 400

Answer 2

To find Alysse's total salary function, we need to determine the formula for her pay based on the information given. We know that she receives a monthly base pay plus commission on all that she sells. We can use the two data points given to create a system of equations and solve for the base pay and commission rate:

When Alysse sells $500 of merchandise, her pay is $515:
Base pay + Commission rate × $500 = $515
Base pay + Commission rate × 500/500 = 515/500
Base pay + Commission rate = 1.03

When Alysse sells $900 of merchandise, her pay is $607:
Base pay + Commission rate × $900 = $607
Base pay + Commission rate × 900/500 = 607/500
Base pay + 1.8 × Commission rate = 1.214

We can solve this system of equations by subtracting the first equation from the second equation, which eliminates the base pay variable:

1.8 × Commission rate - Commission rate = 1.214 - 1.03
0.8 × Commission rate = 0.184
Commission rate = 0.23

Using the first equation, we can solve for the base pay:

Base pay + 0.23 × $500 = $515
Base pay = $515 - $115
Base pay = $400

Therefore, Alysse's total salary function, s(x), when she sells x dollars of merchandise is:

s(x) = $400 + 0.23x

This means that her base pay is $400 per month and she earns a commission of 23% on all the merchandise she sells. For example, if she sells $1000 worth of merchandise in a month, her total pay would be:

s($1000) = $400 + 0.23($1000) = $630

So her total pay increases as she sells more merchandise, reflecting the commission she earns on each sale.