Question

A salesperson is paid a flat rate plus a fixed percentage of her sales. Last month, she sold $16,000 worth of goods and was paid $1,600. Two months ago, she had $12,000 in sales and was paid $1,400. This month she sold $11,000 worth of goods. How much will she be paid?​

Answer 1

1350

Explanation:

(Note: this method is not the best to use in future problems, please refer to the other answer if you want something better to use.)

16,000-12,000=4,000

1,600-1,400=200

To find the rate of change in 1000s:

200/4 = 50

Essentially this means the rise is 50 and the run is 1000, so, just remove $50 from the payment from 2 months ago to find your answer

Answer 2

She will be paid $1,350

Explanation:

Linear Modeling

Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The linear function can be expressed in the slope-intercept format:

y=mx+b, where m and b are constants.

The payments for a salesperson will be linearly modeled. There are two known points: When the sales were $16,000, the payment was $1,600. This makes the point (16,000;1,600).

We also know when the sales were $12,000, the payment was $1,400. The point is (12,000;1,400)

Let's use the points to find the values of m and b.

Using (16,000;1,600):

1,600=m*16,000+b

Using (12,000;1,400):

1,400=m*12,000+b

Subtracting both equations:

200=16,000m-12,000m

200=4,000m

Solving:

m=200/4,000=0.05

Using the first equation and the value of m:

1,600=0.05*16,000+b

1,600=800+b

Solving:

b=800

The equation is now complete:

y=0.05x+800

She sold $11,000 this month, so the payment is:

`y=0.05\cdot 11,000+800`

Y=550+800=1,350

She will be paid $1,350