... vacant If he puts6books on each table he will have 3books left over. Find the numbers of books?
Answers (1)
t = total number of tables
In the first scenario Rohan puts exactly 9 books on one table, then another 9 books on the next until he runs out of books. When he is finished, he has two tables left with no book on either of these.
9 (t - 2) ## The number of books is apparently a multiple of 9.
In the second scenario he places 6 books on each table and has 3 books left. All the tables are used and there is a surplus of 3 books.
6t + 3.
As both terms describe the distribution of his books on a not changing number of tables, we can formulate the equation:
9(t - 2) = 6t + 3
9t - 18 = 6t + 3
3t = 21
t = 7
Now let's plug in this value for the number of tables into both terms
9(t - 2) -> 9 (7 - 2) = 9 * 5 = 45 books
6t + 3 -> 6 * 7 + 3 = 42 + 3 = 45 books
Rohan has 7 tables and 45 books.