Question

A merchant could sell one model of digital cameras at list price and receive$162 for all of them. If he had three more cameras, he could sell each onefor $9 less and still receive $162. Find the list price of each camera.

Answer 1

GIven data:

A merchant could sell one model of digital cameras at list price and receive $162 for all of them.

If he had three more cameras, he could sell each one for $9 less and still receive $162.

To Find the list price of each camera.

Let Price = P and Quantity = Q

PQ = 162

(P-9)(Q + 3) = 162 ...(1)

From the first equation,

Q=162/P

Then,(P-9)(162/P+3)=162

`\begin{gathered} \mleft(P-9\mright)((162)/(P)+3)=162 \\ 3P-(1458)/(P)+135=162 \\ \text{ X P on both sides} \\ P\cdot P-(1458)/(P)P+135P=162P \\ 3P^2-1458+135P=162P \\ P=27,\: P=-18 \\ \end{gathered}`

price acnnot be negative so conside P = 27.

`\begin{gathered} \mleft(27-9\mright)\mleft(Q+3\mright)=162 \\ (\left(27-9\right)\left(Q+3\right))/(18)=(162)/(18) \\ Q+3=9 \\ Q+3-3=9-3 \\ Q=6 \end{gathered}`

Hence P= 27 and Q=6.