Question

Three consecutive integers are such that when they are taken in decreasing order and multiplied by 3,4 and 5 respectively, they add up to 154. find these numbers.​

Answer 1

Given:

• Three consecutive numbers are taken in decreasing order and multiplied by 3,4 and 5 respectively.
• These numbers gives add up to 154

To Find:

• What are those three consecutive numbers?

Solution:

In this question, we are given that when three consecutive numbers are taken in decreasing order and multiplied by 3,4 and 5 respectively, we get 154.

☆ Let suppose that three consecutive numbers are x, (x + 1), (x + 2)

When we write it in decreasing order, we get:

(x + 2) > (x + 1) > x

According to given condition:

3(x + 2) + 4(x + 1) + 5x = 154

→ 3x + 6 + 4x + 4 + 5x = 154

→ 12x + 10 = 154

→ 12x = 154 - 10

→ 12x = 144

→ x = 144/12

→ x = 12

Hence,

• $\small{\bf{1}^{st}~number~=~12}$
• $\small{\bf{2}^{nd}~number~=~12 + 1 ~=~ 13}$
• $\small{\bf{3}^{rd}~number~=~12 + 2 ~=~14}$

Therefore,

• $\large{\underline{\boxed{\bf{\red{Numbers~are~12,13,14}}}}}$

Answer 2

Answer:

• The numbers are 12,13,14 respectively

Step-by-step explanation:

Stated:

• Three consecutive integers are such that
• when they are taken in decreasing order and multiplied by 3,4 and 5 respectively
• they add up to 154

To Attain:

• The value of the numbers

Let us assume:

• 1st number = x
• 2nd number = x + 1
• 3rd number = x + 2

According to the question:

⟶ 3( x + 2 ) + 4 ( x + 1 ) + 5 ( x ) = 154

Solution:

⟶ 3x + 6 + 4x + 4 + 5x = 154

⟶ 3x + 4x + 5x + 6 + 4 = 154

⟶ 12x + 10 = 154

⟶ 12x = 154 - 10

⟶ 12x = 144

⟶ x = 144/12

⟶ x = 12

Therefore,

• 1st number = 12
• 2n number = 12 + 1 = 13
• 3rd number = 12 + 2 = 14