Let x = the number of books.
If there are 5 story books for every 3 science books, we can use the following representation
# of storybooks = 5/8 x
# of science books = 3/8 x
From the problem, we know that the # of picture books also equals 3/8 x
Adding 50 more picture books gives us the following:
3/8 x + 50 = 5/8 x
Multiply both sides by 8 to clear fractions
3x + 400 = 5x
400 = 2x
200 = x
So there are 5/8 * 200 = 1000/8 = 125 story books
3/8 * 200 = 600/8 = 75 science books
and now that 50 books have been added to the picture book stock, a total of 125 picture books
