Problem 7

A man bought a watch, a chain, and a locket for $216. The watch and locket together cost three times as much as the chain, and the chain and locket together cost half as much as the watch. Find the price of each item.

Solution

a) Let W, C, and L denote the costs of the watch, chain, and locket, respectively. We are given:

W+C+L=216 , W+L=3*C , C+L=W/2

b) From W+L=3*C, express L as L=3*C-W

c) Substitute L=3*C-W into W+C+L=216:

W+C+(3*C-W)=216 ⇒4*C=216 ⇒C=54.

d) Use C+L=W/2 with L=3C-W:

54+(3⋅54-W)=W/2

Compute:

54+162-W=216-W=W/2

Multiply by 2:

432-2*W=W ⇒432=3*W ⇒ W=144.

e) Find L:

L=3⋅54-144=162-144=18.

Answer: Watch $144, Chain $54, Locket $18