Three consecutive multiples of 8 is 888. Find the multiples. 8. 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
Answers
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(x+2)
.
It is given that the sum of all the three consecutive multiples of 8 is 888.
Then writing as follows:
⇒8x+8(x+1)+8(x+2)=888
⇒8x+8x+8x+8+16=888
⇒24x+24=888
⇒24x=888−24
⇒24x=864
⇒x=86424
⇒x=36
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a)
Therefore the first multiple of 8 is 8x
, by substituting the value of x in the equation we get,
⇒8×36=288
.
Therefore the second multiple of 8 is 8(x+1)
, by substituting the value of x in the equation we get,
⇒8(36+1)=296
.
Therefore the second multiple of 8 is 8(x+2)
, by substituting the value of x in the equation we get, ⇒8(36+2)=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.