Question

please help I'm pretty much dying over here...
Your favorite coffee place charges $4.75 for a large sized latte. There is a fixed cost of $1,650 to enable the business to serve large lattes each month and an additional cost of $1.45 for every latte made.
1.) write an equation that represents the revenue (R) for selling x lattes.
2.) write an equation that represents the total cost (C) for selling x lattes in one moth.
3.) write a simplified equation that represents the total profit (p) for selling x lattes in one month.
4.) how many lattes do they need to sell in order to break even?

Answer 1

First write out what they need to pay that is independent of the number of lattes they sell, and then write out what cost is dependent on the number of lattes sold.

Answer 2

they need to pay 1650+1.45x ???

Answer 3

well, no. Ok, tell me their profit on ONE latte

Answer 4

their profit on one latte would be $4.75-$1.45= $3.30 ?

Answer 5

correct. that should be your answer to A :\[\huge R(x) = (4.75-1.45)x=3.30x\]

Answer 6

Now for the total cost, we have to factor in that 1650. Do you know how?

Answer 7

would I subtract the equation I already have from it?

Answer 8

Actually, the equation you wrote up there, is the answer to B:
\[\huge \color{blue} {C(x)=1650+1.45x}\]

Answer 9

Also, my above equation R(x) doesn't factor in the 1650 because the question is ambiguous as to whether it should be included or not

Answer 10

Oh nope, that's part 3 P(x)

Answer 11

Total profit looks like:
\[\huge \color{red}{P(x)=(4.75-1.45)x-1650}\]

Answer 12

I was just about to type that! I think I'm getting it...

Answer 13

but the break even point, I don't know how to even start with that

Answer 14

Oh that's the easy part. In order for them to break even, they need to make at least $1650 on the lattes they sell! So the equation is: \[\huge\color{blue}{(4.75-1.45)x=1650}\]

Answer 15

Solve for x!

Answer 16

Pass Medal????????????????????????????????????????????????????

Answer 17

i got x= -1134.66..... is this right?

Answer 18

@Rizags ???????

Answer 19

No that is not right. You need to solve parenthesis first, then divide both sides

Answer 20

ohhh I wrote the equation wrong. I got 500. is this right?

Answer 21

\[(4.75-1.45)x=1650\]\[3.30x=1650\]\[\large \frac{3.30x}{3.30}=\frac{1650}{3.30}\]\[\huge \color{red}{x=500}\]

Answer 22

Yes, medal fan plz

Answer 23

yayyyy thank you so much!

Answer 24

np