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

(a) To find out how many custom necklaces can be manufactured from 311.75 ounces of gold, when each necklace requires 3 5/8 ounces of gold, we first need to convert 3 5/8 ounces to a decimal. 5/8 as a decimal is 0.625, so 3 5/8 ounces is equal to 3 + 0.625, which is 3.625 ounces.

We divide the total amount of gold in stock (311.75 ounces) by the amount of gold required for each necklace (3.625 ounces):

Number of necklaces = 311.75 ounces / 3.625 ounces per necklace

Let's do the math:

Number of necklaces = 311.75 / 3.625 ≈ 86.0345...

Since we can't have a fraction of a necklace, we round down to the nearest whole number. Therefore, we can make 86 necklaces.

(b) To find out how much the gold in each necklace is worth, we multiply the amount of gold in each necklace by the current selling price of gold per ounce.

Value of gold in each necklace = 3.625 ounces * $1,050 per ounce

Let's calculate the value:

Value of gold in each necklace = 3.625 * 1,050 ≈ $3,806.25

Therefore, the gold in each necklace is worth approximately $3,806.25.

Answer 2

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

Explanation:

(a) Number of necklaces

3⁵/₈ = 3.625

`\text{No. of necklaces} = 311.75\text{ oz} * \frac{\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} * \frac{\text{14K}}{\text{24K}} = \text{2.1146 oz}`

Pure 24K gold is worth $1050/oz.

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