Hayden L.
asked • 11/08/21I have no idea what the answer is to this!
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?
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1 Expert Answer
Raymond B. answered • 08/19/23
Tutor
5
(2)
Math, microeconomics or criminal justice
d + r+ c = 1075
d = 3r
c = 105+r
3 equations 3 unknowns
use substitution elimination or matrix algebra
3r +r + 105+r = 1075
5r = 1075-105 = 970
r = 970/5 = 194 rock songs
d = 3r = 3(194) = 582 disco records
c = r+105 = 194+105 = 299 country songs
d+r+c= 582+194+299= 1075
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Julie K.
Hi Hayden. Let's assign dance D, rock R, and country C. D + R + C = 1075. C = R + 105. D = 3R. 3R + R + R + 105 = 1075. 5R + 105 = 1075. 5R = 1075 - 105. 5R = 970. R = 970 ÷ 5. R = 194. D = 3 × 194 = 582. C = R + 105 = 194 + 105 = 299. D + C + R = 1075. Therefore, 582 songs are dance, 194 are rock, 299 were country songs.11/08/21