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

The total number of books is 1020.

Explanation:

Denote the books by their first letter.

From the provided information:

• 
  `S=(3)/(4)A`
• 
  `C=(1)/(4)T`
• 
  `H=(1)/(5)T`
• 
  `H = A-80`

Compute the expression of T as follows:

`H = A-80\\\\(1)/(5)T=A-80\\\\T=5A-400...(i)`

Compute the value of C in terms of A:

`C=(1)/(4)T\\\\C=(1)/(4)* {5A-400}\\\\C=(5)/(4)A-100...(ii)`

Compute the value of A as follows:

Use expressions (i) and (ii):

`T=S+C+H+A\\\\5A-400=(3)/(4)A+(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* 220)-80\\\\T=1100-80\\\\T=1020`

Thus, the total number of books is 1020.