SOLUTION: A chemist has one solution that is 20% acid and a second that is 50% acid. How many gallons of each should be mixed together to get 10 gallons of a solution that is 30% acid?

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Question 18345: A chemist has one solution that is 20% acid and a second that is 50% acid. How many gallons of each should be mixed together to get 10 gallons of a solution that is 30% acid?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The Chemist needs to add x gals. of 20% acid soluton to (10-x) gals. of 50% acid solution to make 10 gals. of 30% acid solution. Change the percents to decimals then write the equation from the problem description.
20% = 0.2
30% = 0.3
50% = 0.5
%280.2%29x+%2B+%280.5%29%2810-x%29+=+%280.3%29%2810%29 Simplify and solve for x.
0.2x+%2B+5+-+0.5x+=+3
-0.3x+%2B+5+=+3 Subtract 5 from both sides.
-0.3x+=+-2 Divide both sides by -0.3
x+=+%28-2%29%2F%28-0.3%29
x = 6 2/3 gals.
10-x = 10-6 2/3 = 3 1/3 gals.
Answer:
The Chemist will need to mix 6 2/3 gallons of 20% acid solution with 3 1/3 gallons of 50% acid solution to make 10 gallons of 30% acid solution.