Answer:
Gold - $33, Silver - $5, Copper - $0.02
Step-by-step explanation:
Let $x be the price of one gram of gold, $y - price of 1 g of silver and $z - price of 1 g of copper.
1. The first alloy is 75% gold, 5% silver, and 20% copper, so in 100 g there are 75 g of gold, 5 g of silver and 20 g of copper. If 100 g of the first alloy costs $2500.40, then
75x+5y+20z=2500.40
2. The second alloy is 75% gold, 12.5% silver, and 12.5% copper, so in 100 g there are 75 g of gold, 12.5 g of silver and 12.5 g of copper. If 100 g of the first alloy costs $2537.75, then
75x+12.5y+12.5z=2537.75
3. The third alloy is 37.5% gold and 62.5% silver, so in 100 g there are 37.5 g of gold and 62.5 g of silver . If 100 g of the first alloy costs $1550.00, then
37.5x+62.5y=1550.00
Solve the system of three equations:
Find all determinants
So,