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, the system of inequalities could represent the values of a and b

option A

Step-by-step explanation:

Here we have , 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, We need to find which system of inequalities could represent the values of a and b . Let's find out:

Let two numbers be a and b where b>a . Now ,

• The sum of two positive integers, a and b, is at least 30

According to the given statement we have following inequality :

⇒ $a+b\geq 30$

• The difference of the two integers is at least 10

According to the given statement we have following inequality :

⇒ $b-a\geq 10$

⇒ $b-a+a\geq 10 +a$

⇒ $b\geq 10 +a$

Therefore , Correct option is A) a + b ≥ 30,  b ≥ a + 10

Answer 2

Answer:

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'

Answer: b + a ≥ 30 and b ≥ a + 10

Option A

Step-by-step explanation: