Question

Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers. please tell in a short and easy way

Answer 1

Answer:

Let the three consecutive integers be x, x+1, and x+2.

According to the question, 2x+3(x+1)+4(x+2)=74

\Rightarrow\ 2x+3x+3+4x+8=74⇒ 2x+3x+3+4x+8=74

\Rightarrow\ 9x+11=74⇒ 9x+11=74

\Rightarrow\ 9x+11-11=74-11⇒ 9x+11−11=74−11

[Subtracting 11 from both sides]

\Rightarrow\ 9x=63⇒ 9x=63

\Rightarrow\ \frac{9x}{9}=\frac{63}{9}⇒  

9

9x

​  

=  

9

63

​  

 

[Dividing both sides by 9]

x = 7

Hence first integer = 7, second integer

= 7 + 1 = 8 and thirs integer = 7 + 2 = 9

Step-by-step explanation:

Answer 2

7 and 8 and 9

Step-by-step explanation:

let the numbers be x (x+1) (x+2)

then 2×x+3(x+1)+4(x+2)=74

2x+3x+3+4x+8=74 ( opening brackets)

9x+11 =74

9x=74-11

9x=63

x=63/9

x=7

x+1= 7+1

=8

x+2 =7+2

=9

the three consecutive numbers are 7 and 8 and 9

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