Question

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?

Answer 1

Dance (D) + Rap (R) + Country (C) = 1,075 songs
D = 3R
C = R + 105

RAP
Subtract 105 from both side:
(3R) + R + (R + 105) = 1,075
-105 -105

Combine all R's:
(3R) + R + R = 970
5R = 970

Divide both sides by 5:
5R = 970
/5 /5
R = 194

DANCE
D = 3(R)
D = 3(194)
D = 582

COUNTRY
C = R + 105
C = 194 + 105
C = 299

So, the DJ has a total of 194 rap songs, 582 dance songs, and 299 country songs.