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 $2500.40, 100 g of the second alloy costsnbsp $ 2537.75, and 100 g of the third alloy costs $ 1550.00, how much does each metal cost?

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,

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

step-by-step explanation: