Question 51789
An auto service center has ten fifty-five gallon drums of 90% ethylene glycol, a common antifreeze fluid used in car radiators. The service center also has eight fifty-five gallon drums of 40% ethylene glycol solution as well. The manager wants to mix appropriate amounts of these two solutions to make 100 gallons of a 65% ethylene glycol concentration. How many gallons of the 90% solution will she need? 
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90% Fluid DATA:
Let amount of 90% fluid be "x"
Amount of active ingredient is 0.90x gallons.
40% Fluid DATA:
Amount of 40% fluid is "100-x" gallons.
Amount of active ingredient is 0.40(100-x)= 40-0.4x
Mixed Fluid DATA:
Amount is 100 gallons.
Amount of active ingredient is 0.65(100)= 65 gallons
EQUATION:
active + active = active
0.90x + 40-0.4x = 65
Multiply thru by 100 to get:
90x + 4000-40x=6500
50x = 1500
x=30 gallons of 90% fluid
100-x=70 gallons of 40% fluid
Cheers,
Stan H.