Question

A coffee 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.

Answer 1

N(p) = -120p + 850

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.

`m = (y_2 -y_1)/(x_2-x_1)`--------------------(2)

`y_1` = number of lattes sold currently = 490

`y_2` = number of lattes sold previously = 490 - 30

`x_1` = cost of lattes sold currently = 3.00

`x_2` = cost of lattes sold previously = 3.00+0.25

Substituting the values in eq(2)

Now, m =
`([(490-30)-490])/([(3.00+0.25)-3.00])`

m =
`(460-490)/(3.25-3.00)`

m =
`(-30)/(0.25)`

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 = -120 * 3.00 +c`

490 = -360 + c

490+360 = c

c = 850

Thus

N(p) = -120p + 850