Question 27475
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