Question

Three consecutive integers are such that when they are taken in increasing order and multiplied by $2,3and4$ respectively, they add up to $74$. Find these numbers.

Answer 1

Let the three consecutive integers are $‘\mathrm{I}’,‘\mathrm{I}+1’\mathrm{Ind}‘\mathrm{I}+2’.$

According to the given details, the equation becomes

$2I+3(I+1)+4(I+2)=74$

$2I+3I+3+4I+8=74$

$9I+11=74$

$9I=74–11$

$9I=63$

$I=63/9$

$I=7$

Thus, the integers are:

First integer: $I=7$

Second integer : $I+1=8$

Third integer : $I+2=9$

Hence, the integers are $7,8,9$.