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. Numbers are $6,5$ and $10$
• B. Numbers are $7,8$ and $9$
• C. Numbers are $3,3$ and $5$.
• D. Numbers are $9,16$ and $19$

Answer 1

The correct option is B Numbers are $7,8$ and $9$

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

According to the given condition, we have
$2\times x+3\times (x+1)+4\times (x+2)=74\Rightarrow 2x+3x+3+4x+8=74\Rightarrow 9x+11=74\Rightarrow 9x=74-11\Rightarrow 9x=63\Rightarrow x=\frac{63}{9}=7$

Hence, other numbers are $x+1=7+1=8$ and $x+2=7+2=9$.
Hence, the numbers are $7,8$ and $9$.