SOLUTION: 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

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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?
a. 10
b. 20
c. 30
d. 40
e. 50
f. 60
g. 70
h. 80
i. 90
j. none of these
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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.