SOLUTION: A services station owner wants to mix up some 35 percent antifreeze. He wants to use up his current supply of 100 gallons of 20 percent antifreeze and add enough 40 percent antifre

Question 1135518: A services station owner wants to mix up some 35 percent antifreeze. He wants to use up his current supply of 100 gallons of 20 percent antifreeze and add enough 40 percent antifreeze to bring the mixture up to 35 percent. How many gallons of 40 percent antifreeze should he add?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x equal the number of gallons of 40 percent antifreeze.

100 * .20 + x * .40 = .35 * (x + 100)

simplify to get 20 + .40 * x = .35 * x + .35 * 100.

simplify further to get 20 + .4x = .35x + 35.

subtract 20 from both sides of this euation and subtract .35x from both sides of this equation to get .4x - .35x = 35 - 20.

simplify to get .05x = 15.

solve for x to get x = 300.

100 * .20 + 300 * .40 = 20 + 120 = 140.

140 / 400 = .35 * 100 = = 35%.

he will need 300 gallons of 40% antifreeze to mix with 100 gallons of 20% antifreeze to get 400 gallons of 35% antifreeze.

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Here is a shortcut alternative to the traditional algebraic solution method shown by the other tutor. If you understand it, it will get you to the answer to any mixture problem like this much faster and with far less effort.

(1) You are starting with 20% antifreeze and adding 40% antifreeze, until the mixture is 35% antifreeze.
(2) 35% is three-fourths of the way from 20% to 40%; therefore, 3/4 of the mixture needs to be what you are adding.
(3) So 1/4 of the mixture is what you started with; since that was 100 gallons, you need to add 300 gallons of the 40% antifreeze to get the desired mixture.
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