Respuesta :

thepingu

Answer:

[tex]\huge\boxed{2}[/tex]

Step-by-step explanation:

In order to find the two consecutive numbers, we have to note that a consecutive number is one that is just after the previous.

Such: 4, 5, 6 are consecutive. 12, 69, 42 are not.

Therefore - we can represent our first number as [tex]x[/tex] and our second as [tex](x+1)[/tex].

Let's make an equation based on the problem.

"The sum of two consecutive integers"

  • [tex]x + (x+1)[/tex]

"3 times their difference"

  • [tex]3(x - (x+1))[/tex]

We can now set these equal to each other.

  • [tex]x + (x+1) = 3(x - (x+1))[/tex]

Let's solve for x.

  • [tex]2x + 1 = 3(1)[/tex] (Combine like terms)
  • [tex]2x+1=3[/tex] (Multiply the right side)
  • [tex]2x = 2[/tex] (Subtract 1 from both sides)
  • [tex]x=1[/tex] (Divide both sides by 2)

Now we know that our first number is 1. Therefore, since our second number is one greater, our second number will be [tex]1+1=2[/tex].

The question asks for the larger number. 2 is larger than 1, therefore 2 is our answer.

Hope this helped!

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