percentage problem

**talanih** · January 14th 2013, 01:18 PM

A company did a study to determine the percent of books that were returned on time. Of the 2000 previously checked books, the number that was returned on time were 300 greater than the number that were not returned on time. what percent of the books in the study were returned on time? How would I set this up?

**abender** · January 14th 2013, 02:36 PM

Let $x$ be the number of books returned on time, so that $(x-300)$ is the number of books NOT returned on time.

$x+(x-300)=2000 \implies 2x-300=2000 \implies 2x=2300 \implies x=\tfrac{2300}{2}=1150$

Since 1150 of the 2000 books were returned on time, the percentage of books returned on time is $\frac{1150}{2000}\times 100\%$

**talanih** · January 15th 2013, 11:32 AM

thank you. I received 57.5%

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