Question 1180731
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Linda needs 10 gallons of solution that is 60% antifreeze. She has a solution
that is 90% antifreeze and another that is 50% antifreeze. How much of each
should she use?
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If v gallons of the 90% then 10-v gallons of the 50%


pure antifreeze account!
{{{90v+50(10-v)=60*10}}}


{{{9v+5(10-v)=60}}}
{{{9v+50-5v=60}}}
{{{4v=10}}}
{{{highlight(v=5/2=2&1/2)}}}{{{gallons}}} for the 90%
-
{{{highlight(7&1/2)}}}{{{gallons}}} for the 50%








For ANY such general two-part mixture percents problem
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Linda needs M gallons of solution that is T% antifreeze. She has a solution
that is H% antifreeze and another that is L% antifreeze. How much of each
should she use?
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v for the H% material
M-v for the L% material


{{{highlight_green(Hv+L(M-v)=TM)}}}


{{{Hv+LM-Lv=TM}}}
{{{Hv-Lv=TM-LM}}}
{{{(H-L)v=M(T-L)}}}

{{{highlight(v=M((T-L)/(H-L)))}}}