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If Lulu had 15u green buttons at first, she had 30u red buttons.

After giving 1/3 of red buttons and 4/5 of green buttons, she was left with 2*30u/3 = 20u red buttons and 15u/5 = 3u green buttons.

3u + 20u = 368

u = 16

45u = 45 * 16 = 720

She had 720 buttons at first.

 

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