Question

The sum of two positive integers, a and b, is at least 30. The difference of the two integers is at least 10. If b is the greater integer, which system of inequalities could represent the values of a and b?

Answer 1

a+b > 30

b-a > 10

hope it helps :)

Answer 2

`a+b\geq 30\\b-a\geq 10\\b>a`

Explanation:

Givens

• The sum of two positive integers is at least 30.
• Their difference is at least 10.
• b is greater than a.

With this information, we can find a system of inequalities. Remember that "at least" means that the sum of these number is 30 or more, and their difference is 10 or more. So

`a+b\geq 30\\b-a\geq 10\\b>a`

The solution of this system is attached. Remember that the solution of a system of inequalities is a graphic solutions, the intersection of all three areas is the solution.

However, the problem is just asking for the system that could represent this situation. So, the answer is

`a+b\geq 30\\b-a\geq 10\\b>a`