Alice's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
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A$$\frac{1}{2}$$
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B$$\frac{1}{3}$$
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C$$\frac{1}{4}$$
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D$$\frac{1}{5}$$
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E$$\frac{1}{6}$$