Answer For problem

Question

Charles has a large book collection. Half of them are fantasy, one quarter are biographies, one eighth are mystery and 6 are books about sports. How many books does he have in all and how many of each genre?

Answer 1

Let's use the variable x to represent the TOTAL number of books in the collection.

Then we can write the following equation to represent the genres:

1 x+ 1 x + 1 x + 6 = x

2 4 8

The least common denominator for 2 , 4, and 8 is 8. Then combine like terms and use inverse operations to solve for x:

4 x+ 2 x + 1 x + 6 = x

8 8 8

7 x + 6 = x

8

7 x + 6 - 7 x = x - 7 x

8 8 8

6 = 1 x

8

48 = x

The total number of books will be 48.

Half of 48 is 24; there will be 24 FANTASY books

One-fourth of 48 is 12: there will be 12 BIOGRAPHY books.

One-eighth of 48 is 6; there will be 6 MYSTERY books.

There are 6 SPORTS books.