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7 November, 10:52

A particular alloy is made of two metals. The density of one of the metals (call it metal A) is 3.0 g/cm3. The density of the other metal (call it metal B) is 5.0 g/cm3. If the density of the alloy is 4.0 g/cm3, what must be the percent composition of the alloy in terms of metal A and metal B?

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  1. 7 November, 10:59
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    50 % A and 50 % B

    Explanation:

    The densities of the metals for the alloy are additive according to the composition of the alloy, so we can establish the following relation:

    Density of alloy = A x Density of A + B x density of B

    where A and B are the percents divided by 100, and we do not need to concern with the units of densities since they appear in both sides of the equation.

    Thus,

    4 = 3 A + 5 B

    But B = 1 - A:

    4 = 3 A + 5 (1 - A) ⇒ 4 = 3A + 5 - 5A

    4 = - 2A + 5 ⇒ - 2A = - 1 ⇒ A = 1/2 = 0.50

    B = 1 - 0.50 = 0.50

    Therefore the % composition is 50 % metal A + 50 % metal B
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