There were some Romance and Fantasy novels in a second-hand bookstore. The number of Romance novels was 3/5 of the number of Fantasy novels. After an equal number of fiction and Romance were sold, the ratio of the number of Romance to the number of Fantasy novels left was 5:9. There were 240 books altogether at first. How many books were sold altogether?
R = Romance novels
F = Fantasy novels
The number of Romance novels was 3/5 of the number of Fantasy novels means:
R / F = 3 / 5
Cross multiply
5 R = 3 F
R = 3 / 5 F
R = 0.6 F
There were 240 books altogether at first means:
R + F = 240
Replace R by 0.6 F in this equation
0.6 F + F = 240
1.6 F = 240
F = 240 / 1.6
F = 150
R = 0.6 • 150 = 90
There were150 Romance and 90 Fantasy at first.
Mark the number of books with x.
Since the number of books sold is the same, it will be:
( R - x ) / ( F - x ) = 5 / 4
( 90 - x ) / ( 150 - x ) = 5 / 9
Agsin cross multiply.
9 • ( 90 - x ) = 5 ( 150 - x )
810 - 9 x = 750 - 5 x
810 - 750 = - 5 x + 9 x
60 = 4 x
x = 60 / 4
x = 15
A total of 15 + 10 = 30 books were sold.