Three consecutive integers are such that when they are taken in decreasing order and multiplied by 3,4 and 5 respectively, they ad

2 thoughts on “Three consecutive integers are such that when they are taken in decreasing order and multiplied by 3,4 and 5 respectively, they ad”

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,

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

   Therefore,

   • [tex]\large{\underline{\boxed{\bf{\red{Numbers~are~12,13,14}}}}}[/tex]

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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

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