Question

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

Answer 1

Hint: Given that the sum of three consecutive multiples of 8 is 888. We have to find the three consecutive numbers which are multiples of 8. Taking the first multiple as \[8x\] and then writing the consecutive numbers, adding all the three consecutive numbers and equating it to 888 and finding the value of \[x\] leads us to the final answer.

Complete step-by-step solution -
Let the first multiple of 8 be \[8x\].
The second consecutive multiple of 8 be \[8(x+1)\].
The third consecutive multiple of 8 be \[8\left( x+2 \right)\].
It is given that the sum of all the three consecutive multiples of 8 is 888.
Then writing as follows:
\[\Rightarrow 8x+8(x+1)+8\left( x+2 \right)=888\]
\[\Rightarrow 8x+8x+8x+8+16=888\]
\[\Rightarrow 24x+24=888\]
\[\Rightarrow 24x=888-24\]
\[\Rightarrow 24x=864\]
\[\Rightarrow x=\dfrac{864}{24}\]
\[\Rightarrow x=36\] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a)
Therefore the first multiple of 8 is \[8x\], by substituting the value of x in the equation we get,
\[\Rightarrow 8\times 36=288\].
Therefore the second multiple of 8 is \[8(x+1)\], by substituting the value of x in the equation we get,
\[\Rightarrow 8\left( 36+1 \right)=296\].
Therefore the second multiple of 8 is \[8\left( x+2 \right)\], by substituting the value of x in the equation we get, \[\Rightarrow 8\left( 36+2 \right)=304\].
If we add up all the three consecutive multiples of 8 we get 288+296+304 = 888

Note: This is a direct problem with the main step of writing the consecutive numbers as x, x+1, x+2 and then doing all the mathematical operations results in a final solution. For further checking if we add all the three multiples should equal to the value given.