The city library donated some books to a class. If each student takes 4 books. there will be 20 books left. If 3 students do not take a book and the rest of the students take 5 books each, there will be no books left. How many books were donated to the class?
Let "x" be the number of students in the class, and "b" be the number of books donated to the class.
We are given two conditions:
If each student takes 4 books, there will be 20 books left. This can be expressed as: x * 4 + 20 = b
If 3 students do not take a book and the rest take 5 books each, there will be no books left. This can be expressed as: (x - 3) * 5 = b
Now, we have a system of two equations:
- x * 4 + 20 = b
- (x - 3) * 5 = b
We can solve this system of equations to find the values of "x" and "b."
First, let's simplify equation 2:
5x - 15 = b
Now, we have the system:
- x * 4 + 20 = b
- 5x - 15 = b
Since both equations equal "b," we can set them equal to each other:
x * 4 + 20 = 5x - 15
Now, solve for "x":
4x + 20 = 5x - 15
Subtract 4x from both sides:
20 = x - 15
Add 15 to both sides:
x = 35
So, there are 35 students in the class. Now, we can find the number of books donated (b) using either of the original equations. Let's use the first one:
x * 4 + 20 = b 35 * 4 + 20 = b 140 + 20 = b b = 160
Therefore, 160 books were donated to the class.
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