A tailor had some buttons. She used 2/3 of the buttons for some shirts and 1/4 of the remainder for some dresses. She bought another 1428 buttons and had twice the number of buttons she had at first. How many buttons had she at first?

Answer: D. 816 buttons

Let the starting number of buttons be X.
She used 2/3, so 1/3 was left (the remainder).
She used 1/4 of that remainder for dresses: (1/4) * (1/3) = 1/12 of the total.
Total used = 2/3 + 1/12 = 8/12 + 1/12 = 9/12 (which is 3/4).
Buttons remaining before buying more = 1/4 of X.
Equation: (1/4) * X + 1428 = 2 * X.
Solve: 1428 = 1.75 * X (which is 7/4 * X).
X = (1428 * 4) / 7 = 816.

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