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Question

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.


Solution

Let the three consecutive integers be $$n,n+1,n+2$$ respectively.

According to the problem,

$$2n+3(n+1)+4(n+2)=74$$

or, $$9n+11=74$$

or, $$9n=63$$

or, $$n=7$$.

So the numbers are $$7,8,9$$.

Mathematics

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