Question

Three consecutive integers are such that when they qre taken in increasing order and multiplied by2,3and4respectivelu,they add up to 74.find these numbets

Answer 1

Let these Three consecutive numbers are X, Y, and Z.

so Y = X+1, and Z = Y+1 = X+2

A/q,

        2X+3Y+4Z = 74

OR,  2X+3(X+1)+4(X+2) = 74

OR,  2X+3X+4X+3+8 = 74

OR,   9X = 74-11

OR,    X = 63/9 = 7

Therefore numbers are X = 7, Y = 7+1 = 8, and Z = 8+1 = 9

 

There's an alternate method too:

let the three integers be x, x+1, x+2

then according to the question

 2x + 3(x +1) + 4 (x+2) = 74

2x + 3x + 3 + 4x + 8 = 74

9x + 11 = 74

9x = 74 - 11

9x = 63 

x = 63 ÷ 9 

x = 7 

 

 

 

so the first integer = 7

second integer(x+1)  = 7+1

                                  = 8

third integer(x+2) = 7+2

                            = 9 

Or, 

Let the three consecutive integers be x, x+1and x+2. 
According to the question, 2x+3(x+1)+4(x+2)=74 
=> 2x+3x+3+4x+8=74

=> 9x+11=74

=>9x+11-11=74-11 [Subtracting 11fromboth sides] 
=> 9x=63

=> 9x/9=63/9 [Dividing both sides by9] 
=> x=7 
Hence first integer = 7, second integer=7 + 1 =8and third integer = 7+ 2= 9.

Hope This Helps :)