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?

“The sum is at least 30” means a + b ≥ 30. Since b is the greater integer and the difference is at least 10, b must be at least 10 more than a, so b ≥ a + 10. Together, these inequalities are choice A: a + b ≥ 30 and b ≥ a + 10.

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