## The sum of three consecutive multiples of 11 is 72. Find these multiples of 11.

Question

The sum of three consecutive multiples of 11 is 72. Find these multiples of 11.

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1 month 2021-08-12T13:38:12+00:00 1 Answer 0 views 0

1. Step-by-step explanation:

The sum of three consecutive numbers is 72. What are the smallest of these numbers.

Let n = the first of three consecutive numbers.

Let n + 1 = the second consecutive number, and …

Let n + 2 = the third consecutive number.

Since we’re given that: “the sum of three consecutive numbers is 72,” then we can now translate this statement mathematically into the following equation to be solved for the unknown number n:

n + (n + 1) + (n + 2) = 72

n + n + 1 + n + 2 = 72

Collecting like-terms on the left, we get:

3n + 3 = 72

3n + 3 – 3 = 72 – 3

3n + 0 = 69

3n = 69

(3n)/3 = 69/3

(3/3)n = 69/3

(1)n = 23

n = 23

Therefore, ,…

n + 1 = 23 + 1 = 24 and

n + 2 = 23 + 2 = 25

CHECK:

n + (n + 1) + (n + 2) = 72

23 + (24) + (25) = 72

23 + 24 + 25 = 72

72 = 72

Therefore, the three consecutive numbers whose sum is 72 are 23, 24, and 25, and 23 is obviously the smallest.