Question

Three times the second of three consecutive even integers is twelve less than twice the sum of the first and third integers.Find the largest even integers

Answer 1

Answer:

The largest even integer is 14.

Step-by-step explanation:

Given:

Three times the second of three consecutive even integers is twelve less than twice the sum of the first and third integers.

Now, to find the largest even integers.

As, 2 is an even number.

Let an even integer be $2x.$

So, the three consecutive even integers are:

$2x,\ 2x+2,\ and\ 2x+4.$

Now, we have to add two to get next even number.

Thus, 3 times the second one of these is:

$3(2x + 2) \\= 6x + 6$

Now, the sum of the first and third ones are:

$2x + 2x + 4 \\= 4x + 4$

So, the twice the sum of the first and third integers is less than twelve:

$2(4x+4)-12\\=8x+8-12\\=8x-4$

Now, 3 times the second is 12 less than twice the sum of the other two:

$6x+6=8x-4$

Getting the variables on one side and the number on other:

$6+4=8x-6x$

$10=2x$

Dividing both sides by 2 we get:

$5=x$

$x=5.$

Now, the even numbers we get are:

$2x=2\times 5=10\\2x+2=2\times 5+2=10+2=12\\2x+4=2\times 5+4=10+4=14.$

Thus, the third number is the largest number which is 14.

Therefore, the largest even integer is 14.