+0

0
1
261
1

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.

Jan 18, 2020

#1
+25532
+2

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.

$$\begin{array}{|rcll|} \hline \dfrac{N-460}{p-3.25} &=& \dfrac{490-460}{3-3.25} \\\\ N-460 &=& (p-3.25)*\dfrac{490-460}{3-3.25} \\\\ N &=& 460+(p-3.25)*\dfrac{490-460}{3-3.25} \\\\ N &=& 460+(p-3.25)*\dfrac{30}{-0.25} \\\\ N &=& 460-(p-3.25)*\dfrac{30}{0.25} \\\\ N &=& 460-p*\dfrac{30}{0.25}+3.25*\dfrac{30}{0.25} \\\\ N &=& 460-p*\dfrac{30}{0.25}+390 \\\\ N &=& 850-p*\dfrac{30}{0.25} \\\\ N &=& 850-p*120 \\\\ \mathbf{N} &=& \mathbf{850 - 120p} \\ \hline \end{array}$$

Jan 18, 2020