If three times the smaller of two consecutive integers is added to four times the larger, the result is 102. find the smallest interger

Two consecutive integers are n and n+1 and of course n+1>n.

3n+4(n+1)=102  perform indicated multiplication on left side

3n+4n+4=102  combine like terms on left side 3n+4n=7n

7n+4=102  subtract 4 from both sides

7n=98  divide both sides by 7

n=14

So the smaller integer is 14.

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