Word 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

1. Let x = total # of books in the collectionooks
2. 0.5x = fantasy books
3. 0.25x = biography books
4. 0.125x = mystery books
5. 6 books are about sports
6. x = 0.5x + 0.25x + 0.125x + 6
7. x = 0.875x + 6
8. .125x = 6
9. x = 6/.125
10. x = 48
11. Double-check your work when you can
1. 0.5x = 0.5(48) = 24
2. 0.25x = 0.25(48) = 12
3. 0.125x = 0.125(48) 6
4. 24 + 12 + 6 + 6 = 48
5. The answer checks out

Answer 2

What I Know

• 1/2: fantasy
• 1/4: biography
• 1/8:mystery
• 6: sports
• HOW MANY BOOKS TOTAL?

 

First, let's find the LCD (Least Common Denominator) to change our fractions: LCD: 8

 

1/2=4/8: fantasy

1/4=2/8: biography

1/8=1/8:mystery

6: sports

 

Second, let's add up the fractions to isolate the fraction that will be equal to 6!

4/8 + 2/8 + 1/8 = 7/8 books : fantasy+biography+mystery

 

THIS MEANS 1/8 OF THE TOTAL NUMBER OF BOOKS ARE SPORTS BOOKS!

 

Since 6 books = 1/8 of the total books, use this to figure out the total number of books and how many per genre!