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? a. a + b ≥ 30 b ≥ a + 10 b. a + b ≥ 30 b ≤ a – 10 c. a + b ≤ 30 b ≥ a + 10 d. a + b ≤ 30 b ≤ a – 10

Start with the difference between the two integers

If b is greater than a, then we can write 'b - a ≥ 10' or 'b ≥ a + 10'

Then we have 'b + a ≥ 30'

b + a ≥ 30 and b ≥ a + 10

Option A

The sum of the two integers is at least 30. This means that the sum could be 30 or greater.
Therefore, the first equation is: a + b ≥ 30 > equation I

The difference between them is at least 10 and b is greater than a. This means that b-a could be 10 or more.
Therefore,
b-a ≥ 10
b ≥ 10 + a > equation II

comparing equations I and II to the choices we have, we will find that the correct choice is (a)