SOLUTION: an auto mechanic needs 24 gallons of ani-freeze with a 30 percent glycol concentration. he has on hand only anit-freeze with a 40 percent glycol concentration and one with a 10 pe

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Question 505087: an auto mechanic needs 24 gallons of ani-freeze with a 30 percent glycol concentration. he has on hand only anit-freeze with a 40 percent glycol concentration and one with a 10 percent glycol concentration. How much of the 40 percent should he mix with the 10 percent to get the 24 gallons of 30 percent solution he needs?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the required number of gallons of the 40% glycol solution. This is to be added to (24-x) gallons of the 10% glycol solution to obtain 24 gallons of 30% glycol solution. The equation to solve for x is:
0.4x+0.1(24-x) = 0.3(24)
0.4x+2.4-0.1x = 7.2 Simplify.
0.3x+2.4 = 7.2
0.3x = 4.8
x = 16 gallons and (24-x) = 8 gallons.
The mechanic will need to mix 16 gallons of the 40% glycol solution with 8 gallons of the 10% glycol solution to obtain 24 gallons of 30% glycol solution.