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}