SOLUTION: Word Problems are so hard for me. I can do them with a calulator, but to write them out in algebriac terms and answering them, I am at a loss. Here is the word problem: Samantha

Question 152357: Word Problems are so hard for me. I can do them with a calulator, but to write them out in algebriac terms and answering them, I am at a loss.
Here is the word problem:
Samantha needs 20 quarts of 50% antifreeze solution in her radiator. She plans to obtain this by nixing some pure antifreeze with an appropriate amount of 40% antifreeze solution. How many quarts of each should she use?
I was thinking 40x . 50 = 20 or maybe 50x + (40 x 20)
I am so new at math, and it is just confusing me to no end!I don't know how to write it, but normally if it's written out I can answer the problem if it's not too complicated.
I would really appreciate any help on this.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Some times, with mixture problems such as this one, it might be a little easier if you think in terms of just the antifreeze rather than the mixture.
You are told that Samantha needs 20 quarts of 50% antifreeze. First, change the percentage to its decimal equavalent (50% = 50/100 = 0.5).
Now 50% of 20 quarts of antifreeze mixture is really 0.5 (20) = 10 quarts of pure antifreeze.
The amount of 40% antifreeze mixture to be added is (20-x) quarts, that is this is the amount, added to the x quarts of pure antifreeze to get the 20 quarts.
Now let x = the amount of pure (100% = 1) antifreeze to be added to (20-x) quarts of 40% antifreeze mixture.
The amount of 40% antifreeze mixture is 0.4(20-x) quarts of antifreeze.
Now you can write an equation to solve for x, the number of quarts of pure antifreeze that Samantha needs.
Perform the indicated multiplication.
Combine the x's
Subtract 8 from both sides.
Finally, didvide both sides by 0.6 to get x by itself.
or x = 3 1/3
So Samantha needs to mix 3 1/3 quarts of pure antifreeze with 20-x = 20-3 1/3 = 16 2/3 quarts of 40% antifreeze mixture to obtain 20 quarts of 50% antifreeze mixture..
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