# Math Investigative Task - calculating the value of metal used in coins.

10B

Part 1

2. The article was written on 11 April 2006.

3.

a) The article mentions that there are 160 pennies in one pound. This means that 160 pennies weigh 0.45359237 kilograms. To find out the weight of one penny in kilograms, divide the weight by the number of pennies. Therefore, it will be 0.45359237 kilograms ÷ 160 pennies = 0.0028349523125 kilograms or 2.8349523125 grams. For ease of calculation, I will be taking it as 2.835 grams.

b) The article mentions that a coin is made up of 97.50% zinc. This means that 97.50% of the total mass of the coin is the mass of the zinc present in the coin. To find out the mass of the zinc, we have to calculate 97.50% of the total mass of one coin. We can calculate this with this calculation: 2.8349523125 x 0.975= 2.7640785046875 grams. For ease of calculation, I will be taking it as 2.764 grams or 0.006 pounds.

c) The article states that a coin is made up of 2.5% copper. This means that 2.5% of the total mass of the coin is the mass of the copper present in the coin. To find out the mass of the copper, we have to calculate 2.5% of the total mass of one coin. We can calculate it with this calculation: 2.8349523125 x 0.025 = 0.0708738078125 grams. For ease of calculation, I will be taking it as 0.071 grams or 0.0015 pounds

4. Ed Yardeni claims that we should wait before we melt the pennies because the price will keep rising and the metals in the penny will be worth more than its face value. To prove this, I will calculate the value of metals before and after the zinc price raised up by \$551 per ton.

Before price hike:

Copper: \$5,690 per ton or \$2.703410526 per pound

Zinc: \$2,930 per ton or \$1.329025645 per pound

Value of Copper in a pound of pennies: 0.025 x 2.703410526 = \$0.067585263

Value of Zinc in a pound of pennies: 0.975 x 1.329025645 = \$1.295800004

Total value of metal in a pound of pennies: 0.067585263 + 1.295800004 = \$1.363385267 or \$1.36

After price hike:

Copper: \$5,960 per ton or \$2.703410526 per pound

Zinc: 2930 + 551 = \$3,481 per ton or \$1.578501448 per pound

Value of Copper in a pound of pennies: 0.025 x 2.703410526 = \$0.067585263

Value of Zinc in a pound of pennies: 0.975 x 1.578501448 = \$1.539038912

Total value of metal in a pound of pennies: 0.067585263 + 1.539038912 = \$1.606624175 or \$1.61

As you can see the total value of the metal in a penny after the price is now more than its face value and this proves Ed Yardeni’s words. Because of this, people will start melting but they will have to melt in a huge quantity to make a decent profit as the metal value of a pound of pennies is only \$0.01 more than its face value.

5. Current price of copper and zinc (as of 18 October, 2011):

• Copper: \$6.90 per kilogram or \$3.1362 per pound
• Zinc: \$1.75 per kilogram or \$0.7959 per pound

To find out the actual manufacturing value of a coin, I will add the cost of copper and zinc.

For copper:

6.90 ÷ 1000 = \$0.0069 per gram of copper

For 0.071 grams, the price would be:

0.0069 x 0.071 = \$0.0004899 for the mass of copper in a coin

For zinc:

1.75 ÷ 1000 = \$0.00175 per gram of zinc

For 2.764 grams, the price would be:

0.00175 x 2.764 = \$0.004837 for the mass of zinc in a coin

For the total price of both metals in a coin:

0.0004899 + 0.004837 = \$0.0053269 or 0.53269 cents

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