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.

• A. $4,5,6$
• B. $5,6,7$
• C. $8,9,10$
• D. $7,8,9$

Answer 1

The correct option is D $7,8,9$

Let the consecutive integers be $x,x+1,x+2$

Given that they are taken in increasing order and multiplied by $2,3,4$.

$\therefore \left(x\right)2+3(x+1)+4(x+2)=74$

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

$9x=74-11=63$

$\therefore x=7$

Then, the numbers would be $x=7$,

$x+1=7+1=8$,

$x+2=7+2=9$.

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