Fred and Bobbie are book collectors, and Fred has twice as many books as Bobbie does. One-fourth of Fred’s books are sig

[VJesus12]

Fred and Bobbie are book collectors, and Fred has twice as many books as Bobbie does. One-fourth of Fred’s books are signed by the authors, and three-fifths of Bobbie’s books are signed by the authors. If Fred and Bobbie combine their collections, what fraction of the books are signed by the authors?

A. 11/30
B. 29/60
C. 23/30
D. 17/20
E. It cannot be determined.

Answer: A

Source: Princeton Review

[deloitte247]

Let the total no of Bobbie's books = x
Fred's book = 2x
Total no. of books = 2x + x = 3x
$$Fred's\ author\ signed\ books=\frac{x}{2}+\frac{3x}{5}=\frac{11x}{10}$$
Fraction of total books signed by authors = (total books signed) / (total no. of books)
$$\frac{\frac{11x}{10}}{3x}=\frac{11x}{10}\cdot\frac{1}{3x}$$
$$\frac{11x}{30x}=\frac{11}{30}\ \ \ \ \ \ Answer\ =\ A$$

[swerve]

Fred and Bobbie are book collectors, and Fred has twice as many books as Bobbie does. One-fourth of Fred’s books are signed by the authors, and three-fifths of Bobbie’s books are signed by the authors. If Fred and Bobbie combine their collections, what fraction of the books are signed by the authors?

A. 11/30
B. 29/60
C. 23/30
D. 17/20
E. It cannot be determined.

Answer: A

Source: Princeton Review

Let's assume that Bobbie has 10 books.

Then Fred has \(2\cdot 10=20\) books
\(\dfrac{1}{5}\cdot 20=5\)
and
\(\dfrac{3}{5}\cdot 10 =6\)

Combine Fraction \(=\dfrac{\text{books signed by author}}{\text{initial no.of books}}\)
\(=\dfrac{11}{30}\)

[Scott@TargetTestPrep]

Fred and Bobbie are book collectors, and Fred has twice as many books as Bobbie does. One-fourth of Fred’s books are signed by the authors, and three-fifths of Bobbie’s books are signed by the authors. If Fred and Bobbie combine their collections, what fraction of the books are signed by the authors?

A. 11/30
B. 29/60
C. 23/30
D. 17/20
E. It cannot be determined.

Answer: A

Solution:

We can let the number of books Fred has be 40. So the number of books Bobbie has is 20. Since 1/4 x 40 = 10 of Fred’s books and 3/5 x 20 = 12 of Bobbie’s books are signed by authors, a total of 22 books are signed by authors. This accounts for 22/60 = 11/30 of their books combined.

Answer: A

[gentvenus]

Let the number of books Fred has be 40.

Number of books Bobbie has is 20.

A total of 22 books are signed by authors.

22/60 = 11/30 of their books.

Answer: A