The Algebra of Gold

1. The Algebra of Gold By Frank J. Antoniazzi Jr.

2. Why study about Gold? • Gold is valuable. • Many people buy gold jewelry. • Gold is useful. • Gold is expensive. • The Golden Rule

3. The Golden Rule Those who have the Gold, make the rules.

4. For you Chemistry Students: Gold is element # 79 a.k.a. Au Atomic weight is 196.9665 Specific Gravity is 19.32 Melting Point is 1064.43 C Boiling Point is 2807 C It has 21 Isotopes

5. How much gold is there? It is said that all the gold in the world will fit in a 50 foot cube, which would only fill about 1/3 of our gym.

6. Pure gold is very soft. For this reason most gold is not pure. It is often mixed with other metals such as copper or silver. Then it is no longer pure gold.

8. The purity of gold is specified by karats. Pure gold is 24 karat gold. Abbreviated as K or KT Karat is sometimes spelled carat

10. 22 karat gold 22 karat gold has 22 parts of gold and 2 parts of some other metal. It is 22/24 or 11/12 pure gold or 91.67% pure gold

11. 18 karat gold 18 karat gold has 18 parts of gold and 6 parts of some other metal. It is 18/24 or 3/4 pure gold or 75% pure gold

12. 14 karat gold 14 karat gold has 14 parts of gold and 10 parts of some other metal. It is 14/24 or 7/12 pure gold or 58.33% pure gold

13. 12 karat gold 12 karat gold has 12 parts of gold and 12 parts of some other metal. It is 12/24 or 1/2 pure gold or 50% pure gold

14. 10 karat gold 10 karat gold has 10 parts of gold and 14 parts of some other metal. It is 10/24 or 5/12 pure gold or 41.67% pure gold

15. Summary of common gold purity • 24K = 100% gold • 22K = 91 2/3% gold • 18K = 75% gold • 14K = 58 1/3 % gold • 12K = 50% gold • 10K = 41 2/3% gold

16. Gold purity is thus a fraction. • To get the percentage of gold divide the gold purity in karats by 24 and then multiply by 100%. • Example: (12K/24K)(100%)=50% • Very simple math: • % of gold = (Karats/24K)(100%)

17. Other information about Au. • Gold can also be measured in fineness. Which means its purity per thousand units. • Thus 900 parts of gold mixed with 100 parts of silver will yield gold that is said to be 900 fine. • Many old American gold coins were 900 fine.

18. Cheaper gold items. • May be called gold filled if it is made from one or more layers of gold and is filled with some other base metal. • To be legal a ‘gold filled’ item must contain at least 5% gold.

19. Gold can also be electroplated to make something look like it is gold. To be legal the electroplating must be at least .000007 inches thick.

20. Plating less than .000007 inches. • If the gold is plated onto something so that the gold is less than .000007 inches thick it can be called gold flashed or gold washed. • When buying a gold item pay attention to these terms. • You could get ripped off! • The term HGE means heavy gold electroplate. • GF means gold filled

21. Buyer Beware Items marked with GF and HGE are worth very little.

23. What is gold worth? • In 1792 was worth $19.39/oz • In 1837 was worth $20.67/oz as set by the US Congress. • In 1934 it was set to $35.00/oz • In 1972 it became worth $38.00/oz • 1n 1973 it was set to be $42.22/ox • By 1980 it was over $800.00/oz • On 28 March 2001 it was $261.20/oz

25. Gold was outlawed by Franklin Delano Roosevelt in 1934 • This happened on 30 January 1934 • The US Constitution still require the use of gold but our government does not often obey the constitution. • Gold became legal to own again in 1975

26. How is gold weighed? • The unit is the Troy Ounce • This is the same as 480 grains • It is also about 31.103 grams • A troy ounce is 1.09714 normal ounces or avoirdupois ounces

28. Only one chemical seems to dissolve gold. • That chemical is called Aqua Regia • It is a mixture of two strong acids, 1 part by volume of concentrated nitric acid mixed with 3 parts by volume of concentrated hydrochloric acid. • The name Aqua Regia was given it by the early alchemists because it could dissolve the king of metals, GOLD.

30. Determining the value of the gold in your jewelry. • You must know the following. • Current price of gold • Weight of your gold in troy ounces • Purity of the gold in karats

31. Example: • You have a 14 karat gold necklace that has a weight of ½ troy ounce. Assume the price of gold is $300.00 per ounce. • Value = ($300/ounce)(14/24)(1/2 ounce) • Value = ($300)(7/12)(1/2) • Value = ($25)(7)(1/2) = ($175)/2 • Value = $87.50 for the gold

32. Why is it worth so little? • A necklace with $87.50 worth of gold probably cost at least $300. • The excess cost was for the manufacturer and the stores doing the selling. • Jewelry is usually a bad investment, but people like it for the look.

33. The same ½ ounce necklace in 10K gold • Value =($300/oz)(10/24)(1/2 oz) • Value =($300/oz)(5/12)(1/2 oz) • Value =($25)(5)(1/2) • Value =($125)/2 • Value = $62.50

34. Example 2 • You have a pair of 18 karat gold earrings that have a weight of 1/20 of an ounce. • Value = ($300)(18/24)(1/20) • Value = ($300)(3/4)(1/20) • Value = ($225)(1/20)=$225/20 • Value = $11.25 • (Most earrings would not weigh that much)

35. Example 3 • You have a pair of 10 karat gold earrings that have a weight of 1/20 of an ounce. • Value = ($300)(10/24)(1/20) • Value = ($300)(5/12)(1/20) • Value = ($125)(1/20)=$125/20 • Value = $6.25 worth of gold

36. To find out the price per ounce you paid for the gold in your jewelry. • As an example we will say that you bought a pair of earrings that were made of 12 karat gold that weigh 1/20 ounce. The cost was only $40.

37. Solve for the gold price • Cost =(Gold price)(purity)(Weight) • $40 = (Gold Price)(12/24)(1 oz/20)$40 = (Gold Price)(1/2)(1 oz/20) • $40 = (Gold Price)(1 oz/40) • $1600/oz = Gold Price • The gold in those earrings would have cost you $1600 per ounce for gold that is currently worth about $300.00 per ounce.

38. Mixing Gold Imagine that you are a jeweler and you have a supply of 12 karat gold and a supply of 18 karat gold, but someone wants you to make 15 ounces of 14 karat gold. How will you do that?

39. What will you use? Obviously since you only have 12 karat gold and 18 karat gold, you must mix them to get 14 karat gold.

40. How much will you need? • Need to make 15 ounces of 14 K • Use X ounces of 12 K • The remainder must come from the 18 K so use (15-X) of the 18 K gold. • Think • What will the equation be?

41. The equation will be: • X(12/24)+(15-X)(18/24)=15(14/24)

42. Solve for X • X(12/24)+(15-X)(18/24)=15(14/24)

43. Solve for X • X(12/24)+(15-X)(18/24)=15(14/24) • Multiply equation by 24 to get • X(12)+(15-X)(18)=(15)(14)

44. Solve for X • X(12/24)+(15-X)(18/24)=15(14/24) • Multiply equation by 24 to get • X(12)+(15-X)(18)=(15)(14) • Rewrite to get this • 12X+18(15-X)=(15)(14) • Distribute the 18 to the 15 and the –X to get • 12X+270-18X=210

45. Solve for X 12X+270-18X=210 12X-18X+270=210 -6X+270=210 -6X+270-270=210-270 -6X+0=-60 (-6X)/(-6)=(-60)/(-6) X=10 this will be in ounces

46. You now know X=10 • This means you need 10 ounces of 12K gold, since X was the variable chosen for the 12K gold needed. • Next find the amount of 18K gold needed to get a total of 15 ounces. • That amount will be (15-X) or (15-10) • Thus you need 5 ounces of 18K gold

47. Your problem is solved. Thru the use of algebra and some common sense we have determined that you can make 15 ounces of 14 karat gold by mixing 10 ounces of 12 karat gold with 5 ounces of 18 karat gold.

48. Just for fun or more practice • How much is that 15 oz of 14 K gold worth on 28 March 2001 when the price of gold was $261.20/ounce? • Use the equation shown earlier to get • Value=($261.20)(14/24)(15) • Value=($261.20)(7/12)(15) • Value=($261.20)(7/4)(5)=$2285.50

49. What would you sell it for? • The gold is worth $2285.50 • You have time and energy involved in doing the work. • You have overhead expenses. • You must pay taxes. • You need to feed you or your family. • You want to keep the customer.

50. Other considerations • The price of gold might increase. • The price of gold might decrease. • Can you make more by selling the gold as 12K and 18K gold? • Etc.