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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