Question

Three consecutive integers are such that when they are taken in increasing order and multiplied by 5,6,and 7 respectively they add up to 74 find these numbers
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Answer 1

Answer:

The three consecutive numbers are:

⇒3,4,5.

Step-by-step explanation:

Let the numbers are x, x+1 and x+2 ,

(Since these are consecutive integers) ,

They are taken in increasing order and multiplied by 2,3 and 4 respectively.

So, x becomes 5x ,

(x+1) becomes 6(x+1) ,

(x+2) becomes 7(x+2).

They add up to 74,so ATQ.

$5x+6(x+1)+7(x+2)=74,\\\\5x+6x+6+7x+14=74,\\\\18x+20=74,\\\\18x=74-20,\\\\18x=54,\\\\x=54/18,\\\\x=3.$

So, the integers are:

x,(x+1),(x+2),

3,(3+1),(3+2),

3,4,5.

$Verification:\\\\5*3+6*4+7*5,\\\\15+24+35,\\\\74.\\\\Hence,\:the\; calculate\: integers\: are\: correct.$

Hope it helps you//.

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