Of all the students in a certain dormitory, ½ are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?
used a double set matrix.
Column 1 = 1 st yr
Column 2 = 2 nd yr
Row 1 = Decl. Major
Row 2 = Not Decl.
Column 3 and Row 3 = Total.
If total = x; 1st yr = 1/2x; 2nd yr = 1/2x
1st yr not decl = 2/5 x
1 st yr decl = 1/2x - 2/5x = 1/10x
2nd yr decl = 3/10 x
2nd yr not decl = 1/2x - 3/10x = 1/5x