The sum of three consecutive multiples of 8 is 888. Find the multiples.

Let us find the multiples of 8 satisfying the given condition.

Answer: The three consecutive multiples of 8 whose sum is 888 are 288, 296, and 304.

Let us simplify the given problem by the nature of multiples of a number.

Explanation:

Method 1:

The multiples of 8 are in the format of 8n.

Let the three consecutive multiples of 8 are 8n - 8, 8n, and 8n + 8

Given that the sum of these multiples is 888.

⇒ (8n - 8) + 8n + (8n + 8) = 888

⇒ 8n + 8n + 8n = 888

⇒ 24n = 888

⇒ n = 888 / 24

⇒ n = 37

⇒ 8n = 296

The multiples of 8 are: 

• 8n - 8 = 296 - 8 = 288
• 8n = 296
• 8n + 8 = 296 + 8 = 304

Method 2:

Consecutive multiples of 8 differ by 8.

So let us assume the three consecutive multiples of 8 be x, x + 8, and x + 16.

Their sum is 888. i.e.,

x + (x + 8) + (x + 16) = 888

Solving this equation for x,

3x + 24 = 888

3x = 864

x = 288;

Then x + 8 = 288 + 8 = 296; x + 16 = 288 + 8 = 304.

Thus, the three consecutive multiples of 8 are 288, 296, and 304.