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?
a + b ≥ 30 b ≥ a + 10

a + b ≥ 30 b ≤ a – 10

a + b ≤ 30 b ≥ a + 10

a + b ≤ 30 b ≤ a – 10

Answer 1

A + b < 30 b < a - 10

Answer 2

Answer:

a + b ≤ 30 b ≥ a + 10

Step-by-step explanation:

Given that the sum of two positive integers, a and b, is at least 30. The difference of the two integers is at least 10.

Since b is greater we can say difference

$b-a\geq 10\\b\geq a+10$

and also since sum of two positive integers is atleast 30 we have next inequality as

$a+b\geq 30$

The system of inequalities can be

a + b ≤ 30 b ≥ a + 10