Question

Three consecutive integers are such that when they are taken in decreasing oder and multiply by 3 4 and 5respectively they add up to 82 find these number?

Answer 1

Given :

• The add up of three consicutive integers = 82.

• Integers are taking decreasing oder and multiply by 3 4 and 5.

To find :

• Three consecutive integers =?

Step-by-step explanation :

Let the numbers are x, x - 1 and x - 2

(Since these are consecutive integers)

They are taken in decreasing order and multiplied by 3 , 4 and 5 respectively,

So x becomes 3x

(x - 1) becomes 4(x - 1)

(x - 2) becomes 5(x - 2)

They add up to 82. [Given]

According to the question :

➮ 3x + 4(x - 1) + 5 ( x - 2) = 82

➮ 3x + 4x - 4 + 5x - 10 = 82

➮ 12x - 14 = 82

➮ 12x = 82 + 14

➮ 12x = 96

➮ x = 96/12

➮ x = 8

Therefore, We get the value of, x = 8.

Hence,

1st integer, 3x = 3 × 8 = 24

2nd integer, 4(x - 1) = 4(8 - 1) = 4 × 7 = 28

3rd integer, 5(x - 2) = 5(8 - 2) = 5 × 6 = 30

Verification :

As we know that,

Add up of all integers = 82

So,

24 + 28 + 30 = 82

82 = 82

L.H.S = R.H.S

Hence, it is verified.

Answer 2

$\sf\large\underline{Let:}$

• $\rm{The\:3\: consecutive\: Number\:are\:x,\:x+1\:x+2}$

$\sf\large\underline{To\: Find:}$

• $\rm{These\: Numbers=?}$

$\sf\large\underline{Solution:}$

• Given here,Three consecutive integers are such that when they are taken in decreasing oder and multiply by 3 4 and 5respectively they add up to 82.]

$\bf\large\underline{A.T.Q}$

$\rm{\implies 5(x)+4(x+1)+3(x+2)=82}$

$\rm{\implies 5x+4x+4+3x+6=82}$

$\rm{\implies 12x+10=82}$

$\rm{\implies 12x=82-10}$

$\rm{\implies 12x=72}$

$\rm{\implies x=6}$

$\sf\large{Hence,}$

$\rm{\implies 1st\: Number=5x=30}$

$\rm{\implies 2nd\: Number=4(x+1)=28}$

$\rm{\implies 3rd\: Number=3(x+2)=24}$

$\sf\large\underline{Verification:}$

$\rm{\implies 5(x)+4(x+1)+3(x+2)=82}$

• Putting the value of x=6 here,]

$\rm{\implies 5(6)+4(6+1)+3(6+2)=82}$

$\rm{\implies 30+28+24=82}$

$\rm{\implies 82=82}$

$\sf\large\underline{Hence,\: Verified:}$