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

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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(6103) About Me  (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.
x+%2B+0.4%2820-x%29+=+0.5%2820%29 Perform the indicated multiplication.
x+%2B+8+-+0.4x+=+10 Combine the x's
0.6x+%2B+8+=+10 Subtract 8 from both sides.
0.6x+=+2 Finally, didvide both sides by 0.6 to get x by itself.
x+=+3.33 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..