Question 53600
Let x represent the first integer; then x+1 is the next consecutive integer.  The equation is {{{(3/5)*(x+1)-(1/2)x=3}}}.  Expanding gives us {{{(3(x+1))/5-x/2=3}}}.  Now multiply both sides by 10 to get {{{6(x+1)-5x=30}}}.  Expanding gives us {{{6x+6-5x=30}}}, which further simplifies to {{{x+6=30}}}.  Subtracting 6 from both sides give us {{{x=24}}}.  That means that our two integers are 24 and 25.  Taking one-half of 24 gives us 12; taking three-fifths of 25 gives us 15.  The difference between 15 and 12 is 3, so we just proved our answer is correct.