Adam is carrying a box full of textbooks for his teacher. It contains math books, which weigh 3 pounds each, and history books, which weigh 2 pounds each. There are 30 books in the box. The total weight, not counting the box itself, is 77 pounds. How many math books are there?

There are 17 math books in the box.

Step-by-step 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

dilation scale factor 2: starting with δabc, draw the dilation image of the triangle with a center at the origin and a scale factor of two. notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). dilation with scale factor 2, multiply by 2.