Question 321890
You have a jug of 40% antifreeze solution in your garage, and you just bought a new container of 100% antifreeze from the auto parts store.  You need to mix up 1 gallon of 50% antifreeze for your car's radiator.  How much of each of the two solutions do you need to use?
Let A be the amount of 40% solution, B the amount of 100% solution.
Volume equation:
1.{{{A+B=1}}}
Concentration equation:
{{{40A+100B=50(1)}}}
2.{{{4A+10B=5}}}
Multiply eq. 1 by (-4) and add to eq. 2,
{{{-4A-4B+4A+10B=-1+5}}}
{{{6B=4}}}
{{{B=4/6}}}
{{{highlight(B=2/3)}}}
Then from eq. 1,
{{{A+2/3=1}}}
{{{highlight(A=1/3)}}}
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Use 1/3 gallon of 40% solution and 2/3 gallon of 100% solution.