Question

The city library donated some children's books to Mr. Clark's first-grade 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?

• A. $120$
• B. $140$
• C. $160$
• D. $175$

Answer 1

The correct option is C $160$

Let the number of students be 's' and the number of books be '$b$'

It is given that if each student takes $4$ books, there will be $20$ books left that is $b=4s+20$

And if $3$ students do not take a book, the rest of the students take $5$ books each that is $b=5(s-3)$

On comparing the value of $b$, we get,

$4s+20=5(s-3)$

$4s+20=5s-15$

$s=20+15$

$s=35$

Now substitute the value of $s$ in $b=4s+20$ as shown below:

$b=4\left(35\right)+20$

$b=140+20$

$b=160$

Therefore $160$ books were donated to the class.

Hence, option C is correct.