question_answer 7)

               Three consecutive integers add up to 51. What are these integers?

Answer:

                Let the three consecutive integers be \[x,\text{ }x+1\] and \[x+2\]. \[\because \]     They add up to 51 \[\therefore \]  \[x+(x+1)\,+(x+2)\,=51\]              \[\Rightarrow \]               \[3x+3=51\] \[\Rightarrow \]               \[3x=51-3\]                         | Transposing 3 to RHS \[\Rightarrow \]               \[3x=48\] \[\Rightarrow \]               \[x=\frac{48}{3}\,=16\]                  | Dividing both sides by 3 \[\Rightarrow \]               \[x+1=16+1=17\] and        \[x+2=16+2=18\]. Hence, the desired integers are 16, 17 and 18. Check:  \[17=16+1\] \[18=17+1\]        | as desired \[16+17+18=51\].