Question

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

Answer 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.