SOLUTION: A 230 second song is divided into three parts. The beginning, middle and end. The beginning is one-sixth as long as the end. The middle is one half as long as the end. Find the

Question 27475: A 230 second song is divided into three parts. The beginning, middle and end. The beginning is one-sixth as long as the end. The middle is one half as long as the end. Find the length of each part. Thanks for your help.
Answer by MOD(6) (Show Source):
You can put this solution on YOUR website!
Hi, I'm here to help.
Here is the equation we will be using.
If x = the end of the song then we can say that x * 1/6 = the beginning and x * 1/2 = the middle.
230 = x + x * (1/6) + x * (1/2)
First we need to find a common denominator. I found that 1 and 2 both go into 6. So I will multiply my first x by 6/6 because 6/6 is still equal to 1. Then I will multiply 1/2 by 3/3 because it is equal to one and it will give me a common denominator of 6 so I can add each of the expressions.
230 = x * (6/6) + x * (1/6) + x * (3/6)
Next add them together.
230 = x * 10/6 or (reduced) 230 = x * (5/3)
Now we must get X by itself.
So you must multiply the reciprocal of 5/3 which is 3/5 to both sides of the equation.
(3/5) * 230 = x * (5/3) * (3/5)
690/5 = x
138 = x
So the end of the song is 138 seconds long. Now to find the length of the middle and the end we can substitute 138 for x in our equation.

230 = 138 + 138 * (1/6) + 138 * (1/2)
230 = 138(End) + 23(Beginning) + 69(Middle)
230 = 230