Question

Average of three consecutive multiples of 3 is 18. Find the numbers

Answer 1

Step-by-step explanation:

Hint: Here, we will first assume the three consecutive multiples are 

3x3x

, 

3(x+1)3(x+1)

and 

3(x+2)3(x+2)

. Take these three consecutive multiples, and then use the given conditions to find the required value.

Complete step-by-step answer:

Given that the sum of the three consecutive multiples of 3 is 72.

Let us assume that the three consecutive multiples of 3 are 

3x3x

, 

3(x+1)3(x+1)

 and 

3(x+2)3(x+2)

.

Simplifying the above consecutive multiples, we get

3x3x

3x+33x+3

3x+63x+6

Now as all these three consecutive numbers are multiples of the number three.

Also, we are given that the sum of these three consecutive multiples is 72, so we have

3x+3x+3+3x+6=723x+3x+3+3x+6=72

Combining the like term in the above equation, we get

⇒9x+9=72⇒9x+9=72

Subtracting the above equation by 9 on each of the sides, we get

⇒9x+9−9=72−9⇒9x=63⇒9x+9−9=72−9⇒9x=63

Dividing the above equation by 9 on each of the sides, we get

⇒9x9=63