Every week Sarah pays for a book and a pen out of her allowance. Last week, Sarah's allowance was $A$ dollars. The cost of her book was $10\%$ of the difference between $A$ and the cost of her pen, while the cost of her pen was $2\%$ of the difference between $A$ and the cost of her book. To the nearest whole percent, what fraction of $A$ did Sarah pay for her book and pen?