Question

Three consecutive EVEN integers have a sum of 60. Find the integers.

Answer 1

Step-by-step explanation:

The sum of 3 consecutive even numbers is 60. What is the smallest of them?

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Let 2n = the smallest consecutive even number.

Let 2(n + 1) = 2n + 2 = the next consecutive even number, and ...

Let 2(n + 2) = 2n + 4 = the third consecutive even number.

Since the sum of these 3 consecutive even numbers is 60, we can write the following equation:

2n + (2n + 2) + (2n + 4) = 60

2n + 2n + 2 + 2n + 4 = 60

By the Commutative Property of Addition, i.e., a + b = b + a, we have on the left side of the equation:

2n + 2n + 2n + 2 + 4 = 60

Now, collecting like-terms on the left side, we get:

(2 + 2 + 2)n + 6 = 60

(6)n + 6 = 60

6n + 6 = 60

Now, in order to solve for n, we begin isolating n on the

If the sum of five consecutive numbers is 435, what will the smallest number be?

The sum of 5 consecutive numbers is 100. What is the smallest number?

The average of four consecutive even numbers is 27. What is the largest of these numbers?

The sum of 4 consecutive even numbers is 86. What is the smallest of them?

The sum of three consecutive even numbers is 168. What is the smallest of the three numbers?

Answer: 18

Algebra:

Let 2n denote the smallest even number of the 3 consecutive numbers where n is an integer to be determined. Then the next two consecutive even numbers are 2n+2 and 2n+4. Therefore, the sum of the 3 consecutive numbers is 2n + 2n+2 +2n+4 = 6n + 6 and this sum is equal to 60 by hypothesis. So we write,

6n + 6 = 60 Dividing through by 6,

n + 1 = 10 Transposing 1 from LHS to right-side,

n = 10 - 1 = 9

Therefore the smallest even number

2n = 18

and the three consecutive numbers are

18, 20, 22

It is easily seen that the sum of the three consecutive numbers so found is

18 + 20 + 22 = 60 (Ver

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Let the 3 consecutive even numbers be x, x+2 and x+4.

Thus, x+x+2+x+4=60 = 3x+6=60 = 3x=60-6

= 3x=54.

As 3x=54,

Therefore, x=54/3 = x=18.

As ‘x’ is the smallest number in the series, therefore the smallest number is 18.

Thus, the next 2 consecutive even numbers should be 20 and 22.

Let's verify:-

18+20+22=60. Thus, this expression satisfies the statement that “ The sum of 3 consecutive even numbers is 60.”

We can see that the smallest number is 18.

Thus, the answer to our question is ‘18’.

Answer 2

Answer:

let the three consecutive even numbers be x x+2 and x+4

thus , x x+2x+4=60

=3x+6=60

3x=60-6

3x=54

there for x=54/3 =x=16

as x is the smallest no. in the series

therefore the smallest no. is 18

thus the next two consecutive no. in the series is 20and 22