Question

At a jewelry store, the price P of a gold necklace varies directly with its length l. Also the weight w of a necklace varies directly with its length. Show that the price of a necklace varies directly with its weight.

Answer 1

\[
P=kl
\]And \[
w = cl
\]so \[
\frac wc=l
\]And \[
P = k\frac wc=\frac kc w
\]

Answer 2

So if you let \(k' = \frac kc\)\[
P=k'w
\]

Answer 3

Which is direct variation.