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.

Answer 1

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.