Question

The sum of three consecutive no.s is 60. What are these integers??

Answer 1

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 left side of the equation by subtracting 6 from both sides:

6n + 6 - 6 = 60 - 6

6n + 0 = 54

6n = 54

Now, finish solving for n by dividing both sides by 6:

(6n)/6 = 54/6

(6/6)n = 54/6

(1)n = 9

n = 9

Therefore, the smallest consecutive even number is:

2n = 2(9)

2n = 18

CHECK:

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

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

2(9) + 2(9) + 2 + 2(9) + 4 = 60

18 + 18 + 2 + 18 + 4 = 60

36 + 2 + 18 + 4 = 60

56 + 4 = 60

60 = 60

Hope it helps

Please mark as brainlist answer

Please mark as brainlist answer

Answer 2

$\bf \large \it \: Hey \: User!!!$

let the three consecutive integers be x, x + 1 and x + 2

we are given that the sum of these integers is 60.

therefore x + x + 1 + x + 2 = 60
>> 3x + 3 = 60
>> 3x = 60 - 3
>> 3x = 57
>> x = 57/3
>> x = 19

hence, the integers are :-

x = 19, x + 1 = 19 + 1 = 20 and x + 2 = 19 + 2 = 21

verification :-

RHS = 60

LHS = x + x + 1 + x + 2

= 19 + 20 + 21

= 60

HENCE LHS = RHS

proved!

$\bf \large \it{Cheers!!!}$