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

Since p varies directly with l,

p = kl     (1)

Also, since w varies directly with l,

w = ml  

or, l = w/m

Substitute in (1), we get,

p = k (w/m)

= (k/m) w

So, the price varies directly with weight.