Question 475488: Two models, A and B, of a statue are made. A has a volume of 32 cm^3 and B has a volume of 56 cm^3. If models A and B have the same mass and the difference in the densities of the material used in making A and B is 1.8 g/cm^3, what is the mass of each model?
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Two models, A and B, of a statue are made. A has a volume of 32 cm^3 and B has a volume of 56 cm^3. If models A and B have the same mass and the difference in the densities of the material used in making A and B is 1.8 g/cm^3, what is the mass of each model?
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density = mass/volume -> mass = density*volume
Since the two masses are equal we can write
d1*V1 = d2*V2
where d = density, V = volume
The difference in the densities is 1.8 -> d1 = d2 + 1.8
[We know d1>d2 since V1
Substitute the V values and the value for d1 in the above equation:
(d2+1.8)*32 = d2*56
24d2 = 57.6
d2 = 2.4
Therefore d1 = 2.4 + 1.8 = 4.2
So densities are 2.4 and 4.2 g/cm^3
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