Question 164811
lets call the younger sister s1 and the older sister s2. now we know that s1+s2=37 and we know that difference between 4 times the older sisters age which we will write as 4s2 and  3 times the younger sister age which we will write as 3s1 equals 43..writing this out this would be 4s2-3s1=43. So solving for s1 in the 1st equation we get s1=37-s2   plugging that into the second equation we get 
4s2-3(37-s2)=43.  now multiply out and simplify...we get 7s2=154 divide by 7 and s2=22        so since s1=37-s2(22) we get s1 is 15

answers younger sister 15
        older   sister 22