A DJ has a total of 1075 dance, rock, and country songs on her system. The dance selection is three times the size of the rock selection. The country selection has 105 more songs than the rock selection. How many songs on the system are dance? rock? country?
+130071 Let R be the number of rock selections
Then 3R = the number of dance selections
And R + 105 = the number of country selections
So
R + 3R + R + 105 = 1075 simplify
5R + 105 = 1075 subtract 105 from both sides
5R = 970 divide both sides by 5
R = 194 rock selections
3R = 3(194) = 582 dance selections
R + 105 = 194 + 105 = 299 country selections
