Question

9. The sum of 3 consecutive even multiples is 72.​

Answer 1

Answer:

22, 24, and 26.

Step-by-step explanation:

Let 2n = the first of three consecutive numbers, where n is an integer.

Let 2n + 2 = the second of three consecutive numbers, and ...

Let 2n + 4 = the third of three consecutive numbers.

The statement: "The sum of three consecutive even numbers is 72" can be translated mathematically into the following equation to be solved for the variable n:

2n + (2n + 2) + (2n + 4) = 72

2n + 2n + 2 + 2n + 4 = 72

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

6n + 6 = 72

Now, subtracting 6 from both sides in order to begin isolating n on the left side, we get:

6n + 6 - 6 = 72 - 6

6n + 0 = 66

6n = 66

Now, divide both sides by 6 as follows in order to finally isolate n on the left side of the equation, thus solving the equation for n:

(6n)/6 = 66/6

(6/6)n = 66/6

(1)n = 11

n = 11

Therefore, ...

2n = 2(11) = 22

2n + 2 = 22 + 2 = 24 and ...

2n + 4 = 22 + 4 = 26

CHECK:

2n + (2n + 2) + (2n + 4) = 72

22 + (24) + (26) = 72

22 + 24 + 26 = 72

46 + 26 = 72

72 = 72

Therefore, the three consecutive even numbers are indeed: 22, 24, and 26.