Question

Jessica is selling books during the summer to earn money for college. She earns a commission on each sale but has to pay for her own expenses.

After a month of driving from neighborhood to neighborhood and walking door-to-door, she figures out that her weekly earnings are approximately a linear function of the number of doors she knocks on.

She writes the equation of the function like this: E(x) = 20x – 50, where x is the number of doors she knocks on during the week and E(x) is her earnings for the week in dollars.
which of the folowing are reasonable interpretations on the y-intercept of Jessica’s function?
A. She can earn $20 per week if she does not knoch on any doors
B. if she does not know on any doors at all during the week. she will lose $150
C. she will lose $20 per week if she does not know on any doors
D. Her expenses are $50

Answer 1

C. she will lose $20 per week if she does not knock on any doors

Explanation:

Given is - Jessica earns a commission on each sale but has to pay for her own expenses.

The weekly earnings are shown as :

`E(x)=20x-50`

where x is the number of doors she knocks on during the week and E(x) is her earnings for the week in dollars.

Now, lets check how much she earns with each door knock or 'x'

When x = 3

`E(3)=20(3)-50`

=> 60-50 = $10

Now x = 4, we get

`E(4)=20(4)-50`

=> 80-50 = $30

Now x = 5, we get

`E(5)=20(5)-50`

=> 100-50 = $50

We can see that with each increased 'x' (door knocks) , Jessica is earning $20.

So, option C is true. Jessica will lose $20 per week if she does not know on any doors.

Answer 2

D is the correct answer. The equation, E(x) = 20x - 50, tells us that Jessica’s earnings (E(x)) for the week is equal to 20 times the number of doors she knocks on, minus 50. The question tells us that she earns commission on each sale but has to pay for her expenses. The -50 represents her expenses.