SOLUTION: A 170 second song is divided into three parts, beginning, middle, and end. Beginning is 1/6 as long as the end. Middle is 1/2 as long as the end. Find the length of each part.

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A 170 second song is divided into three parts, beginning, middle, and end. Beginning is 1/6 as long as the end. Middle is 1/2 as long as the end. Find the length of each part.      Log On


   

Question 506927: A 170 second song is divided into three parts, beginning, middle, and end. Beginning is 1/6 as long as the end. Middle is 1/2 as long as the end. Find the length of each part.
Answer by Maths68(1474) About Me  (Show Source):
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Let
length of end = x
length of beginning = 1/6 * x = x/6
length of middle = 1/2 * x = x/2
length of end + length of beginning + length of middle = Total length
x+(x/6)+(x/2)=170
Multiply by 6 both sides of the equation (6 is LCM of 6, 2)
6*(x+(x/6)+(x/2))=6*170
6x+x+(3*x)=1020
6x+x+3x=1020
10x=1020
Divide by 10 both sides of the equation
10x/10=1020/10
x=102
length of end = x = 102 Seconds
length of beginning = 102/6 = 17 Seconds
length of middle = x/2 = 102/2 = 51 Seconds
length of end + length of beginning + length of middle = Total length
102+17+51=170
170=170