Question 1135611
x = grams of 15% titanium
y = grams of 25% titanium
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Make two equations:
{{{x + y = 100}}}
{{{0.15x + 0.25y = 0.21(100)}}}
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Simplify second equation:
{{{x + y = 100}}}
{{{0.15x + 0.25y = 21}}}
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Multiply second equation by -4:
{{{x + y = 100}}}
{{{-0.6x - y = -84}}}
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Add the equations together:
{{{0.4x = 16}}}
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Solve for x:
{{{x = 40}}}
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x = 40, so that means the metallurgist uses 40 grams of the 15% titanium.  Since x + y = 100 (from our first equation), that means the metallurgist uses 60 grams of the 25% titanium.