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% 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 ​$2340.40​, 100 g of the second alloy costs $2362.75​, and 100 g of the third alloy costs $1350.00​, how much does each metal​ cost?