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Red gold is a gold-copper alloy used to make jewlery. A piece of jewlery made of red gold weighs 8.97g and has a volume of 0.528cm3. Gold has a density of 19.3g/cm3 and copper has a density of 8.96g/cm3. Calculate the percentage by mass of each metal in jewelry. Assume the total volume of the jewelry is the sum of the volumes of the two metals it contains

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Bharathparasad577idn

Percent of gold and copper are 88.2 and 11.8

Red gold is a gold-copper alloy used to make jewelry .

Let the mass  of gold be m1

Let the mass of copper be m2

We are given that m1+m2 =8.97 g

We know that volume is the ratio of mass to density

Thus

m1/d1  + m2/d2 = 0.528 cm3

where d1 and d2 is the density of gold and copper

m1/19.3 + m2/8.96 = 0.528

8.96m1 +19.3 m2 = 0.528 x 19.3 x 8.96 = 91.305

putting m1 = 8.97 - m2

8.96 ( 8.97 - m2 ) + 19.3 m2 = 91.305

80.3712 - 8.96m2 + 19.3 m2 =91.305

10.34 m2 = 91.305-80.3712

m2 = 10.9338 /10.34

      =1.0537gm

m1=8.97-1.0537

    =7.91gm

Therefore, percent of gold = 7.91/8.97 x 100 =88.20%

                 percent of copper = 100-88.2=11.8%

Therefore, percent of gold and copper are 88.2 and 11.8

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