question_answer 8)

                The sum of three consecutive multiples of 8 is 888. Find the multiples.

Answer:

                Let the three consecutive multiples of 8 be \[8x,\,8(x+1)\] and \[8(x+2)\]. \[\because \]     Their sum is 888 \[\therefore \]                  \[8x+8(x+1)+8(x+2)=888\] \[\Rightarrow \]               \[8\{x+(x+1)+(x+2)\}=888\] \[\Rightarrow \]               \[8(3x+3)=888\] \[\Rightarrow \]               \[3x+3=\frac{888}{8}\]                   | Dividing both sides by 8 \[\Rightarrow \]               \[3x+3=111\] \[\Rightarrow \]               \[3(x+1)=111\] \[\Rightarrow \]               \[x+1=\frac{111}{3}\]                     | Dividing both sides by 3 \[\Rightarrow \]               \[x+1=37\] \[\Rightarrow \]               \[x=37-1\]                           | Transposing 1 to RHS \[\Rightarrow \]               \[x=36\] \[\Rightarrow \]               \[8x=8\times 36\,=288\] \[8(x+1)\,=8(36+1)\] \[=8\times 37\,=296\] and \[8(x+2)\,=8(36+2)=8\times 38=304\] Hence, the desired multiples are 288, 296 and 304. Check:  \[288=8\times 36\] \[296=8\times 37=8\times (36+1)\] \[=8\times 36+8=288+8\] \[304=8\times 38=8\times (37+1)\] \[=8\times 27+8=296+8\] \[288+296+304=888\].                   |as desired