Question

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

Answer 1

Answer:

$\huge\boxed{2}$

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 $x$ 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!