20% of the books in a library are fiction. and the rest are non fiction. When 30% of the fiction books and 15% of the non fiction books are borrowed there are 1,148 books left in the library. How many books are 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
Good question 😉
To solve this problem, we need to break it down into steps:
Step 1: Determine the total number of books in the library.
Let's assume the total number of books in the library is represented by 'x'.
Step 2: Calculate the number of fiction books.
Given that 20% of the books in the library are fiction, we can calculate this by multiplying the total number of books by the percentage (0.20):
Number of fiction books = 0.20 * x
Step 3: Calculate the number of non-fiction books.
Since the rest of the books are non-fiction, we can subtract the number of fiction books from the total number of books:
Number of non-fiction books = x - (0.20 * x) = 0.80 * x
Step 4: Determine the number of borrowed fiction books.
Given that 30% of the fiction books are borrowed, we can calculate this by multiplying the number of fiction books by the percentage (0.30):
Number of borrowed fiction books = 0.30 * (0.20 * x) = 0.06 * x
Step 5: Determine the number of borrowed non-fiction books.
Given that 15% of the non-fiction books are borrowed, we can calculate this by multiplying the number of non-fiction books by the percentage (0.15):
Number of borrowed non-fiction books = 0.15 * (0.80 * x) = 0.12 * x
Step 6: Calculate the total number of borrowed books.
The total number of borrowed books is the sum of the borrowed fiction books and the borrowed non-fiction books:
Total number of borrowed books = Number of borrowed fiction books + Number of borrowed non-fiction books
Total number of borrowed books = 0.06 * x + 0.12 * x = 0.18 * x
Step 7: Determine the number of books left in the library.
Given that there are 1,148 books left in the library, we can calculate this by subtracting the total number of borrowed books from the total number of books:
1,148 = x - (0.18 * x)
Now, we can solve the equation to find the value of 'x', which represents the total number of books.
1,148 = x - 0.18x
1,148 = 0.82x
Divide both sides of the equation by 0.82 to solve for 'x':
x = 1,148 / 0.82
x ≈ 1,400
So, the total number of books in the library is approximately 1,400.
Finally, we can substitute the value of 'x' back into Step 6 to find the total number of borrowed books:
Total number of borrowed books = 0.18 * 1,400
Total number of borrowed books ≈ 252
Therefore, approximately 252 books are borrowed.