Gold used to make jewerly is often a blend of gold, silver, and copper. Consider three alloys of these metals.The first alloy is 75% gold, 5% silver, and 20%

Question

(continue) copper. The second alloy is 75% gold, 12.5% silver and 12.5% copper. The third alloy is 37.5% gold and 62.5% silver. If 100 g of the first alloy costs $2655.80, 100g of the second alloy costs $2700.50, and 100 g of the third alloy costs $1687.50, how much does each metal cost? 

Answer 1

0.75 G + 0.05 S + 0.2 C = 26.558

750 G + 50 S + 200 C = 26558 <--- first equation

0.75 G + 0.125 S + 0.125 C = 27.005

750 G + 125 S + 125 C = 27005 <--- second equation

0.375 G + 0.625 S = 16.875

375 G + 625 S = 16875 <--- third equation

================================================

750 G + 50 S + 200 C = 26558

750 G + 125 S + 125 C = 27005

375 G + 625 S = 16875

=============================================

-2 * eq3 + eq2 and -3*eq3 + eq1

will kill the Gold

-1200 S + 200 C = -7192

-1125 S + 125 C = -6745

375 G + 625 S = 16875

================================================

Multiplies first equation by 2.5 and the second

equation by -4; then adds them together; That will

kill the Copper

-3000 S + 500 C = -17980

4500 S - 500 C = 26980

375 G + 625 S = 16875

1500 S = 9000

S = 6

Per third equation, the Gold is

G = (16875 - 625 S)/375

= (16875 - 625 * 6)/ 375

= 13125/375

= 35

Per second equation, the Copper is

4500 S - 500 C = 26980

4500 * 6 - 500 C = 26980

27000 - 500 C = 26980

-500 C = -20

C = -20/-500

= 2/50

= 1/25

= 0.04

The Gold is $35 per ounce

The silver is $6 per ounce

the Copper is $0.04 per ounce

checks against the original equations,

listed here for your convenience:

0.75 G + 0.05 S + 0.2 C = 26.558

0.75 G + 0.125 S + 0.125 C = 27.005

0.375 G + 0.625 S = 16.8

yes, they check out, but you are encouraged

to verify with your calculator.

These answers are correct!

The Gold is $35 per ounce

The silver is $6 per ounce

the Copper is $0.04 per ounce