question_answer 9)

                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:

                Let the three consecutive integers be \[x,\,x+1\] and \[x+2\]. \[\because \]     When taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. \[\therefore \]  \[2x+3(x+1)\,+4(x+2)=74\] \[\Rightarrow \]               \[2x+3x+3+4x+8=74\] \[\Rightarrow \]               \[9x+11=74\] \[\Rightarrow \]               \[9x=74-11\]                      | Transposing 11 to RHS \[\Rightarrow \]               \[9x=63\] \[\Rightarrow \]               \[x=\frac{63}{9}=7\]                       | Dividing both sides by 9 \[\Rightarrow \]               \[x+1=7+1=8\] and        \[x+2=7+2=9\] Hence, the desired numbers are 7, 8 and 9. Check:  \[8=7+1\] \[9=7+2\]            | as desired \[2\times 7+3\times 8+4\times 9\] \[=14+24+36=74\].