Final answer:
To find the total number of books Liam, Sophia, and Madison have, divide their book counts by their greatest common factor, which is 7. Using the distributive property, multiply the quotient by the GCF to find the total number of books. In this case, they have a total of 189 books.
Step-by-step explanation:
To find the total number of books Liam, Sophia, and Madison have, we need to find the greatest common factor (GCF) of their individual book counts. The GCF of 63, 49, and 77 is 7. We can then use the distributive property to determine the total number of books. Let's divide each count by 7: 63 ÷ 7 = 9, 49 ÷ 7 = 7, and 77 ÷ 7 = 11. So, Liam has 9 sets of 7 books, Sophia has 7 sets of 7 books, and Madison has 11 sets of 7 books. Adding them up, we get: 9 sets + 7 sets + 11 sets = 27 sets of 7 books. Finally, we multiply 27 by 7 to get the total number of books: 27 × 7 = 189 books.