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Alenkinab [10]
3 years ago
8

370 second song is divided into three parts, the beginning, the middle, and the end. The beginning is one sixth as long as the e

nd. The middle is one half as long as the end. Find the length of each part
Mathematics
1 answer:
Alex777 [14]3 years ago
3 0

Answer:

Step-by-step explanation:

The main part of the song is the end.  The beginning length is based on the end and so is the middle length.  The beginning length is 1/6 as long as the end, so if the end is our main unknown, x, the beginning is 1/6x.  The middle is one-half as long as the end, so if the end is our main unknown, x, the middle is 1/2x.  The sum of the 3 parts is 370, so:

x+\frac{1}{6}x+\frac{1}{2}x=370

The GCF of those denominators is 6, so multiply through every term by 6 to get rid of the fractions:

(6)x+(6)\frac{1}{6}x+(6)\frac{1}{2}x=(6)370

Simplifying gives us

6x + x + 3x = 2220 and

10x = 2220 so

x = 222

That means that the end is 222 seconds, the bginning is 37 seconds, and the middle is 111 seconds.

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