Answer:
[tex]\boxed{\text{(a) 86 necklaces; (b) \$2220}}[/tex]
Step-by-step explanation:
(a) Number of necklaces
3⁵/₈ = 3.625
[tex]\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}[/tex]
(b) Value of gold in each necklace
There are 3.625 oz of 14K gold in each necklace. Pure gold is 24K.
[tex]\text{Mass of pure gold} = \text{3.625 oz} \times \dfrac{\text{14K}}{\text{24K}} = \text{2.1146 oz}[/tex]
Pure 24K gold is worth $1050/oz.
[tex]\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}}[/tex]