20% books in the library is fiction books and the rest were non fiction books.when 30% of the fiction book and 15% of non fiction books were borrowed,there were 1132 books left.How many books was borrowed?
total number of books in library ---- x
fiction = .2x
non-fiction= .8x
30% of fiction were borrowed, leaving (.7)(.2x) fiction books
15% of non-fiction were borrowed, leaving (.85)(.8x) non-fiction books
(.7)(.2x) + (.85)(.8x) = 1132
.14x + .68x = 1132
.82x = 1132
x = 1132/.82 = 1380.48 ( I was expecting a whole number)
There were 1380 books and 1132 were left, which means
that 1380-1132 or 248 were borrowed
check:
if there were 1380 books
then 276 were fiction and 1104 were nonfiction
30 % of 276 or 83 fiction are out, leaving 193 fiction
15% of 1104 or 166 non-fiction books are out, leaving 938 non-fiction books
sum of remaining books = 193 + 938 = 1131
sum of books borrowed = 83 + 166 = 249
Had I carried decimals in my check calculations, which would be silly since we can't have partial books, the result would have been accurate. The way it is, there seems to be a flaw in the data)
Let's say the total number of books in the library is B.
Given that 20% of the books in the library is fiction books, the number of fiction books can be calculated as 20% of B:
Number of fiction books = 20/100 * B = 0.2B
The remaining books in the library will be non-fiction books, which can be calculated as:
Number of non-fiction books = B - Number of fiction books = B - 0.2B = 0.8B
According to the problem statement, 30% of the fiction books were borrowed. So, the number of borrowed fiction books is:
Borrowed fiction books = 30/100 * Number of fiction books = 0.3 * 0.2B = 0.06B
Similarly, 15% of the non-fiction books were borrowed. So, the number of borrowed non-fiction books is:
Borrowed non-fiction books = 15/100 * Number of non-fiction books = 0.15 * 0.8B = 0.12B
The total number of books borrowed will be the sum of the borrowed fiction and non-fiction books:
Total books borrowed = Borrowed fiction books + Borrowed non-fiction books = 0.06B + 0.12B = 0.18B
Given that there were 1132 books left after borrowing, we can set up the following equation:
B - Total books borrowed = 1132
B - 0.18B = 1132
0.82B = 1132
B = 1132 / 0.82 ≈ 1380.49
Since the number of books cannot be fractional, we can assume the total number of books in the library is 1380.
Now, we can calculate the total number of borrowed books:
Total books borrowed = 0.18B = 0.18 * 1380 ≈ 248.4
Therefore, approximately 248 books were borrowed.
To solve this problem, we can set up an equation based on the information given:
Let's say the total number of books in the library is represented by "x".
Given that 20% of the books are fiction books, we can find the number of fiction books by multiplying x by 20%:
Number of fiction books = 20% of x = 0.2x
The rest of the books, which are non-fiction, can be calculated by subtracting the number of fiction books from the total number of books:
Number of non-fiction books = x - 0.2x = 0.8x
Based on the next piece of information, 30% of the fiction books and 15% of the non-fiction books were borrowed. We can calculate the number of borrowed fiction books and non-fiction books by multiplying the respective percentages by the number of fiction and non-fiction books:
Number of borrowed fiction books = 30% of (0.2x) = 0.3 * 0.2x = 0.06x
Number of borrowed non-fiction books = 15% of (0.8x) = 0.15 * 0.8x = 0.12x
The total number of borrowed books equals the sum of the borrowed fiction and non-fiction books:
Number of borrowed books = Number of borrowed fiction books + Number of borrowed non-fiction books
= 0.06x + 0.12x
= 0.18x
Given that there were 1132 books left after the borrowing, we can subtract this number from the total number of books to find the number of borrowed books:
Number of borrowed books = Total number of books - Number of books left
= x - 1132
Setting these two expressions for the number of borrowed books equal to each other, we can solve for x:
0.18x = x - 1132
Simplifying the equation:
0.18x - x = -1132
-0.82x = -1132
Dividing both sides of the equation by -0.82:
x = -1132 / -0.82
x ≈ 1380.4878
Since the number of books cannot be in decimal form, we would typically round the answer to the nearest whole number. Therefore, the total number of books in the library is approximately 1380.
Now, to find the number of borrowed books, we substitute the value of x into the equation we derived earlier:
Number of borrowed books = 0.18 * 1380
= 248.4
Rounded to the nearest whole number, the number of books borrowed is 248.
So, approximately 248 books were borrowed.