Question

A jewelry store has 311.75 ounces of 14-carat gold in stock.
(a)
How many custom necklaces can be manufactured if each requires
3 5/8 ounces of gold?

86 necklaces

(b) If gold is currently selling for $1,050 per ounce, how much is the gold in each necklace worth (in $)?

Answer 1

Answer:

$\boxed{\text{(a) 86 necklaces; (b) \ 2220}}$

Step-by-step explanation:

(a) Number of necklaces

3⁵/₈ = 3.625

$\text{No. of necklaces} = 311.75\text{ oz} \times \dfrac{\text{1 necklace}}{3.625\text{ oz}} = \textbf{ 86 necklaces}\\\\\text{You can make } \boxed{\textbf{86 necklaces}} \text{ from 311.75 oz of 14K gold}$

(b) Value of gold in each necklace

There are 3.625 oz of 14K gold in each necklace. Pure gold is 24K.

$\text{Mass of pure gold} = \text{3.625 oz} \times \dfrac{\text{14K}}{\text{24K}} = \text{2.1146 oz}$

Pure 24K gold is worth $1050/oz.

$\text{Value of pure gold} = \text{2.1146 oz} \times \dfrac{\text{\ 1050}}{\text{1 oz}} = \textbf{\ 2220}\\\\\text{The value of the gold in each necklace is } \boxed{\textbf{\ 2220}}$