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

Explanation:

Step 1: Define

+a

+b

b is the bigger integer

Step 2: Write inequalities

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

• This means that the combined value, a + b, must be greater than or equal to, ≥, 30.
• a + b ≥ 30

"The difference of the two integers is at least 10."

• We know that the difference must be positive, as it has to be at least, ≥, 10.
• Since b is the greater number, a must be subtracting from it, or else we would get a negative number
• b - a ≥ 10
• b ≥ a + 10