Acoffee shop currently sells 490 lattes a day at $3.00 each. they recently tried raising the by price by $0.25 a latte, and found that they sold 30 less lattes a day. a) assume that the number of lattes they sell in a day, n, is linearly related to the sale price, p (in dollars). find an equation for n as a function of p.

N(p) = -120p + 850

Step-by-step explanation:

Let the number of lattes sold by the coffee shop  be N

and p be the price of each Lattes

The number of lattes (N) sold by a coffee shop is linearly related to the sale price (p).

Now,Let the linear relationship be

N(p) = mp+c, -------------------(1)

where

m is the slope

c is an arbitrary real number.

--------------------(2)

=  number of lattes sold  currently   = 490

 = number of lattes sold  previously  = 490 - 30

=  cost of lattes sold currently = 3.00

 = cost of lattes sold  previously  = 3.00+0.25

Substituting the values in eq(2)

Now, m =

m =

m =

m  = -120.

On substituting m = -160 eq(1), we get

N(p) = -120p+c.

Further, on substituting N = 430 and p = 2.75 , we get

490 = -360 + c

490+360 = c

c = 850

Thus

N(p) = -120p + 850