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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

Respuesta :

Space

Answer:

a + b ≥ 30  b ≥ a + 10

Step-by-step 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

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