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If 2 times the sum of two consecutive even numbers is greater than 94, what is the smallest possible value of the larger number?

Respuesta :

semsee45

Answer:

26

Step-by-step explanation:

Define the variables:

  • 2n = first even number
  • 2n + 2 = consecutive even number

Given information:

  • 2 times the sum of two consecutive even numbers is greater than 94

Create an inequality from the defined variables and the given information:

⇒ 2(2n + 2n + 2) > 94

Solve the inequality:

⇒ 2(4n + 2) > 94

⇒ 8n + 4 > 94

⇒ 8n > 90

⇒ n > 11.25

Therefore:

  • 2n > 22.5
  • 2n + 2 > 24.5

As 2n and 2n+2 are even numbers:

  • smaller number (2n) ≥ 24
  • larger number (2n + 2) ≥ 26

Therefore, the smallest possible value of the larger number is 26.

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