A box contains a mixture of small copper spheres and small lead spheres. The total volume of both metals is measured by the displacement of water to be 423 cm^3 and the total mass is 4.35 kg. What percentage of the spheres are copper?

44.01% of the spheres are copper

Explanation:

mass Cu + mass Pb = 4.35kg =  4.35 x 1000 = 4350g

But

Volume= mass / density

Let the volume of copper be C  

density of  Cu = 8.94 g/cm^3

Mass of copper = 8.94C

Let the volume of Lead be L  

density of  lead = 11.34g/cm^3

Mass of lead  = 11.34L

Since  

mass Cu + mass Pb = 4350kg

therefore

8.94C + 11.34L = 4350g EQN A

also

volume of copper + volume of lead =  423 cm^3

Volume of Lead ,L=423-C

putting the value of C = 423-L in Equation A becomes

8.94C + 11.34L = 4350g

8.94C + 11.34(423-C)= 4350g

8.94C+ 4796.82-11.34C=4350

4796.82-4350=11.34C- 8.94

446.82=2.4C

C= 186.175

Volume of copper = 186.175cm^3

Percentage copper = volume copper / total volume metal x 100/1

= 186.175 cm^3 / 423 cm^3 x 100/1

= 44.01%

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