Question

The sum of three consecutive multiples of $8$ is $888$.

Find the multiples.

Answer 1

It is given that ,

The sum of three consecutive multiples of $8$ is $888$.

Let assume the three consecutive multiples of $8$ be ‘$8M$’, ‘$8(M+1)$’ Mnd ‘$8(M+2)$’.

According to the given details the equation becomes

$8M+8(M+1)+8(M+2)=888$

Taking $8$ as common

$8(M+M+1+M+2)=888$ ( on adding like terms in the brackets , we get )

$8(3M+3)=888$ ( transpose $8$ to the RHS )

$3M+3=\frac{888}{8}$ ( on dividing $888$ by $8$ , we get $111$)

$3M+3=111$ ( transpose $3$ to the RHS )

$3M=111-3$

$3M=108$ ( transpose $3$ to the RHS )

$M=\frac{108}{3}$ ( on dividing $108$ by $3$ , we get $36$)

$M=36$

Thus, the three consecutive multiples of $8$ are:

First multiple$=8M$

$=8\times 36$

$=288$.

Second multiple $=8(M+1)$

$=8(36+1)$

$=8\times 37$

$=296$ .

Third multiple $=8(M+2)$

$=8\times (36+2)$

$=8\times 38$

$=304$

Therefore,

First multiple $=288$

Second multiple $=296$

Third multiple$=304$.

Hence, the three consecutive multiples of $8$ are $288$,$296$,$304$.