Answer:
There are 17 math books in the box.
Explanation:
To determine how many math books and how many history books are in the box, it is necessary to perform the following logical reasoning:
Given that math books weigh 3 pounds, while history books weigh 2 pounds, knowing that there are 30 books in the box and that it contains a total weight of 77 pounds, the difference between the common weight of both types of book must be obtained.
Thus, if the 30 books were 2 pounds (that is, history) the box would weigh 60 pounds, but with 77 pounds there is a surplus of 17 pounds (77 - 60). Since each math book is one pound heavier than the history books, there are 17 math books, while the remaining 13 are history. This is verified by the following calculation:
17 x 3 + 13 x 2 = X
51 + 26 = X
77 = X