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The sum of two consecutive integers is three times their difference. what is the larger number?​

1 Answer

4 votes

Answer:


\huge\boxed{2}

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
x and our second as
(x+1).

Let's make an equation based on the problem.

"The sum of two consecutive integers"


  • x + (x+1)

"3 times their difference"


  • 3(x - (x+1))

We can now set these equal to each other.


  • x + (x+1) = 3(x - (x+1))

Let's solve for x.


  • 2x + 1 = 3(1) (Combine like terms)

  • 2x+1=3 (Multiply the right side)

  • 2x = 2 (Subtract 1 from both sides)

  • x=1 (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
1+1=2.

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

Hope this helped!

User Deesolie
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