A metalworker has a metal alloy that is 20% copper and another alloy that is 60% copper. How many kilograms of each alloy should the metalworker combine to create 80 kg of a 52% copper alloy?

Question

A metalworker has a metal  alloy that is 20% copper and another alloy that is 60% copper. How many kilograms of each alloy should the metalworker combine to create 80 kg of a 52% copper alloy?

anonymous · Answer

Oh ok, assuming that those percentages are mass fractions (thought they were mole fractions), then the problem boils down to a system of equations:

1) m_1(0.2) + m_2(0.6) = (m_3)*0.52
2) m_1 + m_2 = m_3

m_3 = 80, m_1 = kilograms of alloy_1 that should be used, m_2 = kilograms of alloy_2 that should be used. However then there's metals processing issues for the metalworker to make the system homogeneous.