Question

10) Two numbers have a sum that is less than 16 and a product that is more than 36. Illustrate on a graph all the number pairs that satisfy these conditions, and list all the positive integers that satisfy these conditions.

Can someone please explain clearly, step by step, how to solve this question please.

Answer 1

1. For this problem, you must first set up inequalities. Based on this question we can set the inequalities as x + y < 16 and x * y > 36.

2. Use a graphing tool to graph these inequalities. It is shown in the image below.

3. Any point in the intersection (but not on the dashed lines) between the two inequalities is a solution.

4. To list all the positive combinations with integers that satisfy this system, we can test the points out. The positive integers that satisfy these conditions are:

(4, 10); (4, 11); (5, 8); (5, 9); (5, 10); (6, 7); (6, 8); (6, 9); (7, 6); (7, 7); (7, 8); (8, 6); (8, 7); (9, 5); (9, 6); (10, 4); (10, 5); (11, 4)