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After Yixin gave Zack 25% of the money, the total amount of money they had still the same at 15760.

$15760 – $8210 = $7550

80% of Zack spending was $7550

Zack had 10* $7550/8 =  $9437.5 after Yixin gave Zack 25% of her money.

Yixin had $15760 – $9437.5 =$ 6322.5 after giving Zack 25% of her money.

So she had $6322.5 *4/3 $8430 at first.

And Zack had $15760 – $8430 = $7330 at first.

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