Question

There are books in a library, there are 4 different kinds of books. Science books make up 3/4 of art books. Comic books are 1/4 of the total books. History books are 1/5 of the total books. History books are 80 fewer than art books. How many books are in total?

Answer 1

Answer:

The total number of books is 1020.

Step-by-step explanation:

Denote the books by their first letter.

From the provided information:

• $S=\frac{3}{4}A$
• $C=\frac{1}{4}T$
• $H=\frac{1}{5}T$
• $H = A-80$

Compute the expression of T as follows:

$H = A-80\\\\\frac{1}{5}T=A-80\\\\T=5A-400...(i)$

Compute the value of C in terms of A:

$C=\frac{1}{4}T\\\\C=\frac{1}{4}\times {5A-400}\\\\C=\frac{5}{4}A-100...(ii)$

Compute the value of A as follows:

Use expressions (i) and (ii):

$T=S+C+H+A\\\\5A-400=\frac{3}{4}A+\frac{5}{4}A-100+A-80+A\\\\5A-400=4A-180\\\\A=220$

Compute the value of T as follows:

$T=5A-80\\\\T=(5\times 220)-80\\\\T=1100-80\\\\T=1020$

Thus, the total number of books is 1020.