How do you find four consecutive integers whose sum is 114?

1 Answer
Alan P.
Oct 19, 2016

The four numbers are 27, 28,29,and 3027,28,29,and30

Explanation:

Let the smallest number be nn.
Then the four numbers are n, n+1, n+2, and n+3n,n+1,n+2,andn+3
and their sum is
color(white)("XXX")n+(n+1)+(n+2)+(n+3)=4n+6XXXn+(n+1)+(n+2)+(n+3)=4n+6

We are told that this sum is equal to 114114
So
color(white)("XXX")4n+6=114XXX4n+6=114

color(white)("XXX")rarr 4n=108XXX→4n=108

color(white)("XXX")rarr n=27XXX→n=27

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