Question

A jewelry store has 212.75 ounces of 14-carat gold in stock. (a) how many custom necklaces can be manufactured if each requires 2 7/8 ounces of gold? (b) if gold is currently selling for $1,050 per ounce, how much is the gold in each necklace worth (in $)?

Answer 1

Answer:

a. The number of custom necklaces that can be manufactured if each requires 2 7/8 ounces of gold is 74 necklaces.

b. The value of the gold in each necklace is $1761

Step-by-step explanation:

(a) Number of necklaces

2$7/8$ ounces of gold=2.875

No of necklaces=212.75oz x 1 necklaces/2.875oz

                          =74 necklaces

(b)Value of gold in each necklace

There are 2.875 oz of 14K gold in each necklace. Pure gold is 24K.

Mass of pure gold=2.875oz x 14k/24k

                              =1.677083oz

Pure 24K gold is worth $1050/oz.

Value of pure gold=1.677oz x 1050/1oz

                              = 1760.9 dollars

The value of the gold in each necklace is $1761

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Answer 2

a) Number of custom necklaces that can be crafted if each requires 2 7/8 ounces of gold which is 74 necklaces.

b) The gold value of each necklace is $1761

• Algebra is a branch of mathematics that deals with symbols and the rules for using those symbols.  

• In elementary algebra, these symbols (now written in Latin and Greek letters) represent quantities with no fixed value, called variables.  

(a) Number of necklaces

2 7/8 ounces of gold = 2.875

Number of necklaces = 212.75 oz x 1 necklace / 2,875 oz

= 74 necklaces

(b) Gold value in each necklace

There is 2,875 oz of 14k gold in each necklace. Pure gold is 24K.

Mass of pure gold = 2,875 oz x 14k / 24k

= 1.677083oz

Pure 24-karat gold is worth $1,050 per ounce.

Pure Gold Value = 1,677 oz x 1050/1 oz

= $1760.9

The gold value of each necklace is $1761

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