World problem

Question

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 $2120.80, 100 g of the second alloy costsnbsp $ 2150.50, and 100 g of the third alloy costs $ 1300.00, how much does each metal cost?
Gold costs $
Per/g. (Round to the nearest cent as needed.)

Answer 1

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The following has an error or two in the calculations

But if I don't post it, I lose it. For some reason my computer

deletes it, otherwise. I'll be back to correct the errors

Since the problem is very old, I don't suspect it's more than academic at this point.

But if someone sees it and sees the error, feel free to point it out.

And if anyone is relying on the answer, please don't.

Otherwise, in a few hours, I may figure it out.

.75G + .05S +.2 C = 2120.8

.75G + .125S + .125C = 2150.50

.375G + .625 S = 1300

3G/4 + S/20 + C/5 = 2120.8

3G/4 + S/8 + C/8 = 2150.50

3G/8 + 5S/8 = 1300

3 equations, 3 unknowns, use matrix algebra or substitution & elimination method

Multiply 2nd equation by 5 , then subtract 3rd equation from result to eliminate S

15G/4 + 5S/8 + 5C/8 = 10752.5

3G/8 + 5S/8 = 1300

27G/8 +5C/8 = 9452.5 multiply by 1/5

27G/40 + 5C/40 = 1890.50

.Now use the first two equations to similarly eliminate S

Multiply the 1st equation by 1/2 and the 2nd by 1/5, then subtract them

3G/8 + S/40 + C/10 = 1060.4

3G/20 +S/40 +C/40 = 430.10

9G/40 +3C/40 = 630.30 multiply by 3 and subtract 27G/40 + 5C/40 =1690.50

27G/40 +9C/40 =1890.90

27G/40 +5C/40 =1690.50

4C/40 =C/10 = 200.40

multiply by 10 C =$2004

27G/4 + 5C/4 = 16905

27G/4 +5(2004)/4 = 16905

27G/4 5(501) = 16905

27G/4 =16905 -2505

27G/4 = 14400

G = (4/27)(1440) = $213.33

Take the original 3rd equation and substitute for G=213.33

3G/8 +5S/8 = 1300 multiply by 8 to get

3G +5S = 10400

3(213.33) + 5S = 10400

5S = 10400 - 639.99 = 10400 - 6400 = 4000

S = 4000/5 = $800

Gold is $213.33, Silver is $800 and Copper is $2004