The number of library books in a school increased by 20% after it bought new books in may. The number increased by another 20% after a bookstore donated 300 books in June. Find the number of books in the library before it bought new books in May.
n
after buy 1.2 n
after donation 1.2*1.2 n
300 = .2 * 1.2 n
300 = .24 n
n = 1250
Let's assume the number of books in the library before it bought new books in May is "x."
After buying new books in May, the number of books increased by 20%. This can be expressed as:
New number of books in May = x + 0.2x = 1.2x
In June, the number of books further increased by another 20% after a bookstore donated 300 books. This can be expressed as:
New number of books in June = 1.2x + 0.2(1.2x) + 300
Now we can set up an equation to find the value of x:
New number of books in June = x + 0.2x + 300
Replacing the values from above:
1.2x + 0.2(1.2x) + 300 = x + 0.2x + 300
Multiplying 0.2 by 1.2x:
1.2x + 0.24x + 300 = x + 0.2x + 300
Combining like terms:
1.44x + 300 = x + 0.2x + 300
Simplifying:
1.44x + 300 = 1.2x + 300
Subtracting 1.2x from both sides:
0.24x + 300 = 300
Subtracting 300 from both sides:
0.24x = 0
Dividing both sides by 0.24:
x = 0
Therefore, the number of books in the library before buying new books in May is 0. However, this does not seem like a practical answer. There might be a mistake in the given information or in the calculations. Please double-check the information provided and try solving the problem again.
To find the number of books in the library before it bought new books in May, we can work backward.
Let's assume the original number of books in the library before any changes occurred is represented by "X".
After buying new books in May, the number of books increased by 20%, which means the library now has X + 0.20X = 1.20X books.
After the bookstore donated 300 books in June, the total number of books increased by another 20%, which means there are now 1.20X + 0.20(1.20X) = 1.44X books in the library.
We know that 1.44X is equal to the number of books after the June donation, which is also the number of books after the May purchase. So we can set up the equation:
1.44X = X + 300
Let's solve for X:
1.44X - X = 300
0.44X = 300
X = 300 / 0.44
X ≈ 681.82
Therefore, the number of books in the library before it bought new books in May is approximately 681.82 books.