Question 175727
Call the first integer x.  Then the next two can be represented by x+2 and x+4 (think about 2,4,6 as an example).  Then the "sum of the larger two" would be (x+2) + (x+4) and "54 more than the smallest integer" would be x+54.  So we have the equation
{{{(x+2)+(x+4)=x+54}}}
{{{2x+6=x+54}}}
Subtracting x from both sides and subtracting 6 from both sides, we get
{{{x=48}}}
Thus, the three consecutive even integers are 48, 50, and 52.