Question

There are 3 consecutive even integers that sum to 186. What is the value of the greatest integer?

Answer 1

The 3 consecutive even numbers are 60, 62 and 64 and the value of the greatest is 64.

Step-by-step explanation:

If the numbers are consecutive even numbers, it means that the next number will be 2 more than the previous one.

Let the 1st number be x, then other 2 consective numbers will be x + 2 and x + 4.

We're told that the sum of the 3 consecutive even numbers is equal to 186, our equation can then be written as shown below;

`x+(x+2)+(x+4)=186`

Let's go ahead and collect like terms and solve for x;

`\begin{gathered} 3x+6=186 \\ 3x=186-6 \\ 3x=180 \\ x=(180)/(3) \\ \therefore x=60 \end{gathered}`

So our 1st number is 60.

Let's go ahead and find the other 2 numbers;

1st number: x + 2 = 60 + 2 = 62

2nd number: x + 4 = 60 + 4 = 64

So the 3 consecutive even numbers are 60, 62 and 64 and the value of the greatest is 64.