Question

2. The Smiths are starting a Bed & Breakfast business, and invest $3000 to get started. They charge visitors $100/night, of which $20 is used for food, supplies, etc. for the B&B.
-- Write an equation that models this situation.
-- What are the intercepts? Explain the significance of each in the above problem.
x-inercept
y intercept
( I can't figure out which is x and which is y!!!)

Answer 1

So you want the revenue equation? or the profit equation?

Answer 2

which is x and which is y. thats all I need.

Answer 3

well x sounds like the number of visitors

but not sure of y since they don't really state what they want (do they want the cost, revenue, or profit?)

Answer 4

oh x could be the number of nights (for a certain visitor)...hmm not sure, this problem seems like it's missing something

Answer 5

x has to be something that never changes but y is the variable
I guess x would be the $100/night because that stays the same but $20 would depend on how many nights the people stayed....
UGGGHH!!!

Answer 6

no, x is a variable, which means it does change

Answer 7

* bangs head against the wall.

Answer 8

if x = number of nights, then 100x is the amount charged to one visitor for x nights

Answer 9

so the revenue would be y = 100x (this is the amount of money coming in disregarding expenses)

Answer 10

YES.. I think...

Answer 11

if you add on the expenses, then it costs 20x dollars to feed this visitor (and provide other essentials) plus the $3000 invested

so the total cost is 20x+3000


Subtract this from the revenue to get

100x - (20x+3000)

100x-20x-3000

80x-3000


So the profit equation is

y = 80x - 3000

this is only the case if y is the profit

Answer 12

the profit equation because y=mx+b

Answer 13

I think...

Answer 14

@jgurl.3958 What do you mean by " the profit equation because y=mx+b " :/

Answer 15

By the definition of Profit P(x) = Revenue R(x) - Cost C(x)

Answer 16

I am learning y=mx+b

Answer 17

all of the problems on this sheet are y=mx+b

Answer 18

guys, HELP ME!!

Answer 19

I just gave you the answer, not sure what else you're looking for

Answer 20

which on is it

Answer 21

the revenue is y = 100x

the cost is y = 20x+3000

the profit is y = 80x-3000

Answer 22

that's the problem...the question doesn't explicitly ask for any of those (it's too vague)

Answer 23

so idk what they want exactly

Answer 24

IDK either

Answer 25

yeah you're going to have to ask the teacher on this one, she might know what they want

Answer 26

unless there's context elsewhere that's missing?

Answer 27

Its due tomorrow and I wrote the whole problem.

Answer 28

hmm then I'd go with the profit since that's usually the thing most considered (sure cost and revenue are important, but the bottom line is usually the most important -- besides, profit = revenue - cost)

Answer 29

if that's the case, then you would use the equation y = 80x - 3000

Answer 30

thanks but how would you get the 80? and what are the significance of the x and y?

Answer 31

100x - 20x = 80x

Answer 32

x is the number of nights and y is the revenue

Answer 33

i mean, profit

Answer 34

x is the number of nights, y is the profit

Answer 35

and what are the intercepts

Answer 36

to find the y-intercept plug in x = 0 and solve for y

to find the x-intercept plug in y = 0 and solve for x

Answer 37

y=-3000

Answer 38

that's the y-intercept

the y-intercept as a point is (0,-3000)

Answer 39

for the x should I use a decimal or a improper fraction?

Answer 40

hmm I'd go with a decimal since you're dealing with money

Answer 41

and what is the significance of (0,-3000) in the problem? And also (37.5,0)

Answer 42

11/2 dollars doesn't make much sense, but 5.50 dollars does

Answer 43

I got 37.5

Answer 44

(0,-3000) means that for 0 visitors (x = 0) the profit is -3000 dollars (y = -3000)

basically they lose $3,000 if no one shows up

Answer 45

I got 37.5 dollars, not 5.50

Answer 46

5.50 was just a random example of how decimals are better than fractions (when it comes to money)

Answer 47

oh....

Answer 48

yeah sry, just something random

Answer 49

what does (37.5,0) have to do with the problem?

Answer 50

(37.5, 0) means x = 37.5 and y = 0

Remember x = number of nights

Let's assume you can only have a whole number of nights.

So between x = 37 and x = 38, the profit will be 0. This means that the breakeven point occurs between night 37 and night 38.

Answer 51

If you reassign x to be number of visitors who only stay one night, then x = 37 means that you have 37 visitors who stay one night and x = 38 means that you have 38 visitors who stay one night.

Answer 52

what is the 0 though

Answer 53

0 is the profit

Answer 54

its where they break even (they make no money and they lose no money)

Answer 55

so I would say: If 38 people come to the B&B the smiths will lose no money but gain no money?

Answer 56

between 37 and 38, yeah that sounds about right

Answer 57

ok
thanks!

Answer 58

yw