SOLUTION: A 14% ETHANOL SOLUTION IS TO BE MIXED WITH A 45% ETHANOL SOLUTION TO PRODUCE A FINAL SOLUTION WHICH IS 30% ETHANOL.iF THE FINAL SOLUTION IS 100 GALLONS.FIND THE AMOUNT OF EACH SOLU

Question 45656: A 14% ETHANOL SOLUTION IS TO BE MIXED WITH A 45% ETHANOL SOLUTION TO PRODUCE A FINAL SOLUTION WHICH IS 30% ETHANOL.iF THE FINAL SOLUTION IS 100 GALLONS.FIND THE AMOUNT OF EACH SOLUTION NEEDED FOR DELISHA TO MIX.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A 14% ETHANOL SOLUTION IS TO BE MIXED WITH A 45% ETHANOL SOLUTION TO PRODUCE A FINAL SOLUTION WHICH IS 30% ETHANOL.iF THE FINAL SOLUTION IS 100 GALLONS.FIND THE AMOUNT OF EACH SOLUTION NEEDED FOR DELISHA TO MIX.
Start:
Let amount of 45% solution be "x"
Amount of active ingredient is 0.45x.

Add:
Let amount of 14% solution be "y"
Amount of active ingredient is 0.14y.
End up with:
Amount you end up with is 100 gals.
Amount of active ingredient is 0.30(100)= 30 gals.
EQUATIONS:
amt. + amt. = 100 gals
x + y = 100
active + active = 30 gals.
0.45x + 0.14y=30
Solve the 1st equation for x and substitute into the 2nd equation, as follows:
x=100-y
0.45(100-y) + 0.14y = 30
45(100-y) + 14y = 3000
4500-45y+14y=3000
-31y=-1500
y=48.39 gals. (amount of 14% solution)
x=100-48.39=51.61 gals (amount of 45% solution)
Cheers,
Stan H.
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